Solve {l}{1/162x(x-3)(x-6)+1/27(x+3)(x-3)(x-6)}{+1/27x(x+3)(x-6)+10/162x(x+3)(x-3)}

$$\left. \begin{array} { l } { \frac { 1 } { 162 } x ( x - 3 ) ( x - 6 ) + \frac { 1 } { 27 } ( x + 3 ) ( x - 3 ) ( x - 6 ) } \\ { + \frac { 1 } { 27 } x ( x + 3 ) ( x - 6 ) + \frac { 10 } { 162 } x ( x + 3 ) ( x - 3 ) } \end{array} \right.$$

Evaluate

$$\frac{23x^{3}}{162}-\frac{7x^{2}}{18}-\frac{13x}{9}+2$$

Solution Steps

Use the distributive property to multiply \frac{1}{162}x by x-3.

$$\left(\frac{1}{162}xx+\frac{1}{162}x\left(-3\right)\right)\left(x-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply x and x to get x^{2}.

$$\left(\frac{1}{162}x^{2}+\frac{1}{162}x\left(-3\right)\right)\left(x-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{162} and -3 to get \frac{-3}{162}.

$$\left(\frac{1}{162}x^{2}+\frac{-3}{162}x\right)\left(x-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{-3}{162} to lowest terms by extracting and canceling out 3.

$$\left(\frac{1}{162}x^{2}-\frac{1}{54}x\right)\left(x-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of \frac{1}{162}x^{2}-\frac{1}{54}x by each term of x-6.

$$\frac{1}{162}x^{2}x+\frac{1}{162}x^{2}\left(-6\right)-\frac{1}{54}xx-\frac{1}{54}x\left(-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{1}{162}x^{3}+\frac{1}{162}x^{2}\left(-6\right)-\frac{1}{54}xx-\frac{1}{54}x\left(-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply x and x to get x^{2}.

$$\frac{1}{162}x^{3}+\frac{1}{162}x^{2}\left(-6\right)-\frac{1}{54}x^{2}-\frac{1}{54}x\left(-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{162} and -6 to get \frac{-6}{162}.

$$\frac{1}{162}x^{3}+\frac{-6}{162}x^{2}-\frac{1}{54}x^{2}-\frac{1}{54}x\left(-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{-6}{162} to lowest terms by extracting and canceling out 6.

$$\frac{1}{162}x^{3}-\frac{1}{27}x^{2}-\frac{1}{54}x^{2}-\frac{1}{54}x\left(-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine -\frac{1}{27}x^{2} and -\frac{1}{54}x^{2} to get -\frac{1}{18}x^{2}.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}-\frac{1}{54}x\left(-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Express -\frac{1}{54}\left(-6\right) as a single fraction.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{-\left(-6\right)}{54}x+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply -1 and -6 to get 6.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{6}{54}x+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{6}{54} to lowest terms by extracting and canceling out 6.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Use the distributive property to multiply \frac{1}{27} by x+3.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x+\frac{1}{27}\times 3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{27} and 3 to get \frac{3}{27}.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x+\frac{3}{27}\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{3}{27} to lowest terms by extracting and canceling out 3.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x+\frac{1}{9}\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of \frac{1}{27}x+\frac{1}{9} by each term of x-3.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}xx+\frac{1}{27}x\left(-3\right)+\frac{1}{9}x+\frac{1}{9}\left(-3\right)\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply x and x to get x^{2}.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x^{2}+\frac{1}{27}x\left(-3\right)+\frac{1}{9}x+\frac{1}{9}\left(-3\right)\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{27} and -3 to get \frac{-3}{27}.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x^{2}+\frac{-3}{27}x+\frac{1}{9}x+\frac{1}{9}\left(-3\right)\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{-3}{27} to lowest terms by extracting and canceling out 3.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x^{2}-\frac{1}{9}x+\frac{1}{9}x+\frac{1}{9}\left(-3\right)\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine -\frac{1}{9}x and \frac{1}{9}x to get 0.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x^{2}+\frac{1}{9}\left(-3\right)\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{9} and -3 to get \frac{-3}{9}.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x^{2}+\frac{-3}{9}\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{-3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x^{2}-\frac{1}{3}\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of \frac{1}{27}x^{2}-\frac{1}{3} by each term of x-6.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\frac{1}{27}x^{2}x+\frac{1}{27}x^{2}\left(-6\right)-\frac{1}{3}x-\frac{1}{3}\left(-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\frac{1}{27}x^{3}+\frac{1}{27}x^{2}\left(-6\right)-\frac{1}{3}x-\frac{1}{3}\left(-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{27} and -6 to get \frac{-6}{27}.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\frac{1}{27}x^{3}+\frac{-6}{27}x^{2}-\frac{1}{3}x-\frac{1}{3}\left(-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{-6}{27} to lowest terms by extracting and canceling out 3.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\frac{1}{27}x^{3}-\frac{2}{9}x^{2}-\frac{1}{3}x-\frac{1}{3}\left(-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Express -\frac{1}{3}\left(-6\right) as a single fraction.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\frac{1}{27}x^{3}-\frac{2}{9}x^{2}-\frac{1}{3}x+\frac{-\left(-6\right)}{3}+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply -1 and -6 to get 6.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\frac{1}{27}x^{3}-\frac{2}{9}x^{2}-\frac{1}{3}x+\frac{6}{3}+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Divide 6 by 3 to get 2.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\frac{1}{27}x^{3}-\frac{2}{9}x^{2}-\frac{1}{3}x+2+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine \frac{1}{162}x^{3} and \frac{1}{27}x^{3} to get \frac{7}{162}x^{3}.

$$\frac{7}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x-\frac{2}{9}x^{2}-\frac{1}{3}x+2+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine -\frac{1}{18}x^{2} and -\frac{2}{9}x^{2} to get -\frac{5}{18}x^{2}.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}+\frac{1}{9}x-\frac{1}{3}x+2+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine \frac{1}{9}x and -\frac{1}{3}x to get -\frac{2}{9}x.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Use the distributive property to multiply \frac{1}{27}x by x+3.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\left(\frac{1}{27}xx+\frac{1}{27}x\times 3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply x and x to get x^{2}.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\left(\frac{1}{27}x^{2}+\frac{1}{27}x\times 3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{27} and 3 to get \frac{3}{27}.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\left(\frac{1}{27}x^{2}+\frac{3}{27}x\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{3}{27} to lowest terms by extracting and canceling out 3.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\left(\frac{1}{27}x^{2}+\frac{1}{9}x\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of \frac{1}{27}x^{2}+\frac{1}{9}x by each term of x-6.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x^{2}x+\frac{1}{27}x^{2}\left(-6\right)+\frac{1}{9}xx+\frac{1}{9}x\left(-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x^{3}+\frac{1}{27}x^{2}\left(-6\right)+\frac{1}{9}xx+\frac{1}{9}x\left(-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply x and x to get x^{2}.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x^{3}+\frac{1}{27}x^{2}\left(-6\right)+\frac{1}{9}x^{2}+\frac{1}{9}x\left(-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{27} and -6 to get \frac{-6}{27}.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x^{3}+\frac{-6}{27}x^{2}+\frac{1}{9}x^{2}+\frac{1}{9}x\left(-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{-6}{27} to lowest terms by extracting and canceling out 3.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x^{3}-\frac{2}{9}x^{2}+\frac{1}{9}x^{2}+\frac{1}{9}x\left(-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine -\frac{2}{9}x^{2} and \frac{1}{9}x^{2} to get -\frac{1}{9}x^{2}.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x^{3}-\frac{1}{9}x^{2}+\frac{1}{9}x\left(-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{9} and -6 to get \frac{-6}{9}.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x^{3}-\frac{1}{9}x^{2}+\frac{-6}{9}x+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{-6}{9} to lowest terms by extracting and canceling out 3.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x^{3}-\frac{1}{9}x^{2}-\frac{2}{3}x+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine \frac{7}{162}x^{3} and \frac{1}{27}x^{3} to get \frac{13}{162}x^{3}.

$$\frac{13}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2-\frac{1}{9}x^{2}-\frac{2}{3}x+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine -\frac{5}{18}x^{2} and -\frac{1}{9}x^{2} to get -\frac{7}{18}x^{2}.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{2}{9}x+2-\frac{2}{3}x+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine -\frac{2}{9}x and -\frac{2}{3}x to get -\frac{8}{9}x.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{10}{162} to lowest terms by extracting and canceling out 2.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x\left(x+3\right)\left(x-3\right)$$

Use the distributive property to multiply \frac{5}{81}x by x+3.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\left(\frac{5}{81}xx+\frac{5}{81}x\times 3\right)\left(x-3\right)$$

Multiply x and x to get x^{2}.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\left(\frac{5}{81}x^{2}+\frac{5}{81}x\times 3\right)\left(x-3\right)$$

Express \frac{5}{81}\times 3 as a single fraction.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\left(\frac{5}{81}x^{2}+\frac{5\times 3}{81}x\right)\left(x-3\right)$$

Multiply 5 and 3 to get 15.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\left(\frac{5}{81}x^{2}+\frac{15}{81}x\right)\left(x-3\right)$$

Reduce the fraction \frac{15}{81} to lowest terms by extracting and canceling out 3.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\left(\frac{5}{81}x^{2}+\frac{5}{27}x\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of \frac{5}{81}x^{2}+\frac{5}{27}x by each term of x-3.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{2}x+\frac{5}{81}x^{2}\left(-3\right)+\frac{5}{27}xx+\frac{5}{27}x\left(-3\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}+\frac{5}{81}x^{2}\left(-3\right)+\frac{5}{27}xx+\frac{5}{27}x\left(-3\right)$$

Multiply x and x to get x^{2}.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}+\frac{5}{81}x^{2}\left(-3\right)+\frac{5}{27}x^{2}+\frac{5}{27}x\left(-3\right)$$

Express \frac{5}{81}\left(-3\right) as a single fraction.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}+\frac{5\left(-3\right)}{81}x^{2}+\frac{5}{27}x^{2}+\frac{5}{27}x\left(-3\right)$$

Multiply 5 and -3 to get -15.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}+\frac{-15}{81}x^{2}+\frac{5}{27}x^{2}+\frac{5}{27}x\left(-3\right)$$

Reduce the fraction \frac{-15}{81} to lowest terms by extracting and canceling out 3.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}-\frac{5}{27}x^{2}+\frac{5}{27}x^{2}+\frac{5}{27}x\left(-3\right)$$

Combine -\frac{5}{27}x^{2} and \frac{5}{27}x^{2} to get 0.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}+\frac{5}{27}x\left(-3\right)$$

Express \frac{5}{27}\left(-3\right) as a single fraction.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}+\frac{5\left(-3\right)}{27}x$$

Multiply 5 and -3 to get -15.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}+\frac{-15}{27}x$$

Reduce the fraction \frac{-15}{27} to lowest terms by extracting and canceling out 3.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}-\frac{5}{9}x$$

Combine \frac{13}{162}x^{3} and \frac{5}{81}x^{3} to get \frac{23}{162}x^{3}.

$$\frac{23}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2-\frac{5}{9}x$$

Combine -\frac{8}{9}x and -\frac{5}{9}x to get -\frac{13}{9}x.

$$\frac{23}{162}x^{3}-\frac{7}{18}x^{2}-\frac{13}{9}x+2$$

Expand

$$\frac{23x^{3}}{162}-\frac{7x^{2}}{18}-\frac{13x}{9}+2$$

Solution Steps

Use the distributive property to multiply \frac{1}{162}x by x-3.

$$\left(\frac{1}{162}xx+\frac{1}{162}x\left(-3\right)\right)\left(x-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply x and x to get x^{2}.

$$\left(\frac{1}{162}x^{2}+\frac{1}{162}x\left(-3\right)\right)\left(x-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{162} and -3 to get \frac{-3}{162}.

$$\left(\frac{1}{162}x^{2}+\frac{-3}{162}x\right)\left(x-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{-3}{162} to lowest terms by extracting and canceling out 3.

$$\left(\frac{1}{162}x^{2}-\frac{1}{54}x\right)\left(x-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of \frac{1}{162}x^{2}-\frac{1}{54}x by each term of x-6.

$$\frac{1}{162}x^{2}x+\frac{1}{162}x^{2}\left(-6\right)-\frac{1}{54}xx-\frac{1}{54}x\left(-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{1}{162}x^{3}+\frac{1}{162}x^{2}\left(-6\right)-\frac{1}{54}xx-\frac{1}{54}x\left(-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply x and x to get x^{2}.

$$\frac{1}{162}x^{3}+\frac{1}{162}x^{2}\left(-6\right)-\frac{1}{54}x^{2}-\frac{1}{54}x\left(-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{162} and -6 to get \frac{-6}{162}.

$$\frac{1}{162}x^{3}+\frac{-6}{162}x^{2}-\frac{1}{54}x^{2}-\frac{1}{54}x\left(-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{-6}{162} to lowest terms by extracting and canceling out 6.

$$\frac{1}{162}x^{3}-\frac{1}{27}x^{2}-\frac{1}{54}x^{2}-\frac{1}{54}x\left(-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine -\frac{1}{27}x^{2} and -\frac{1}{54}x^{2} to get -\frac{1}{18}x^{2}.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}-\frac{1}{54}x\left(-6\right)+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Express -\frac{1}{54}\left(-6\right) as a single fraction.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{-\left(-6\right)}{54}x+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply -1 and -6 to get 6.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{6}{54}x+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{6}{54} to lowest terms by extracting and canceling out 6.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\frac{1}{27}\left(x+3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Use the distributive property to multiply \frac{1}{27} by x+3.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x+\frac{1}{27}\times 3\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{27} and 3 to get \frac{3}{27}.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x+\frac{3}{27}\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{3}{27} to lowest terms by extracting and canceling out 3.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x+\frac{1}{9}\right)\left(x-3\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of \frac{1}{27}x+\frac{1}{9} by each term of x-3.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}xx+\frac{1}{27}x\left(-3\right)+\frac{1}{9}x+\frac{1}{9}\left(-3\right)\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply x and x to get x^{2}.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x^{2}+\frac{1}{27}x\left(-3\right)+\frac{1}{9}x+\frac{1}{9}\left(-3\right)\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{27} and -3 to get \frac{-3}{27}.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x^{2}+\frac{-3}{27}x+\frac{1}{9}x+\frac{1}{9}\left(-3\right)\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{-3}{27} to lowest terms by extracting and canceling out 3.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x^{2}-\frac{1}{9}x+\frac{1}{9}x+\frac{1}{9}\left(-3\right)\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine -\frac{1}{9}x and \frac{1}{9}x to get 0.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x^{2}+\frac{1}{9}\left(-3\right)\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{9} and -3 to get \frac{-3}{9}.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x^{2}+\frac{-3}{9}\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{-3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\left(\frac{1}{27}x^{2}-\frac{1}{3}\right)\left(x-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of \frac{1}{27}x^{2}-\frac{1}{3} by each term of x-6.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\frac{1}{27}x^{2}x+\frac{1}{27}x^{2}\left(-6\right)-\frac{1}{3}x-\frac{1}{3}\left(-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\frac{1}{27}x^{3}+\frac{1}{27}x^{2}\left(-6\right)-\frac{1}{3}x-\frac{1}{3}\left(-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{27} and -6 to get \frac{-6}{27}.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\frac{1}{27}x^{3}+\frac{-6}{27}x^{2}-\frac{1}{3}x-\frac{1}{3}\left(-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{-6}{27} to lowest terms by extracting and canceling out 3.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\frac{1}{27}x^{3}-\frac{2}{9}x^{2}-\frac{1}{3}x-\frac{1}{3}\left(-6\right)+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Express -\frac{1}{3}\left(-6\right) as a single fraction.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\frac{1}{27}x^{3}-\frac{2}{9}x^{2}-\frac{1}{3}x+\frac{-\left(-6\right)}{3}+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply -1 and -6 to get 6.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\frac{1}{27}x^{3}-\frac{2}{9}x^{2}-\frac{1}{3}x+\frac{6}{3}+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Divide 6 by 3 to get 2.

$$\frac{1}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x+\frac{1}{27}x^{3}-\frac{2}{9}x^{2}-\frac{1}{3}x+2+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine \frac{1}{162}x^{3} and \frac{1}{27}x^{3} to get \frac{7}{162}x^{3}.

$$\frac{7}{162}x^{3}-\frac{1}{18}x^{2}+\frac{1}{9}x-\frac{2}{9}x^{2}-\frac{1}{3}x+2+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine -\frac{1}{18}x^{2} and -\frac{2}{9}x^{2} to get -\frac{5}{18}x^{2}.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}+\frac{1}{9}x-\frac{1}{3}x+2+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine \frac{1}{9}x and -\frac{1}{3}x to get -\frac{2}{9}x.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x\left(x+3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Use the distributive property to multiply \frac{1}{27}x by x+3.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\left(\frac{1}{27}xx+\frac{1}{27}x\times 3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply x and x to get x^{2}.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\left(\frac{1}{27}x^{2}+\frac{1}{27}x\times 3\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{27} and 3 to get \frac{3}{27}.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\left(\frac{1}{27}x^{2}+\frac{3}{27}x\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{3}{27} to lowest terms by extracting and canceling out 3.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\left(\frac{1}{27}x^{2}+\frac{1}{9}x\right)\left(x-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of \frac{1}{27}x^{2}+\frac{1}{9}x by each term of x-6.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x^{2}x+\frac{1}{27}x^{2}\left(-6\right)+\frac{1}{9}xx+\frac{1}{9}x\left(-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x^{3}+\frac{1}{27}x^{2}\left(-6\right)+\frac{1}{9}xx+\frac{1}{9}x\left(-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply x and x to get x^{2}.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x^{3}+\frac{1}{27}x^{2}\left(-6\right)+\frac{1}{9}x^{2}+\frac{1}{9}x\left(-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{27} and -6 to get \frac{-6}{27}.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x^{3}+\frac{-6}{27}x^{2}+\frac{1}{9}x^{2}+\frac{1}{9}x\left(-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{-6}{27} to lowest terms by extracting and canceling out 3.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x^{3}-\frac{2}{9}x^{2}+\frac{1}{9}x^{2}+\frac{1}{9}x\left(-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine -\frac{2}{9}x^{2} and \frac{1}{9}x^{2} to get -\frac{1}{9}x^{2}.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x^{3}-\frac{1}{9}x^{2}+\frac{1}{9}x\left(-6\right)+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Multiply \frac{1}{9} and -6 to get \frac{-6}{9}.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x^{3}-\frac{1}{9}x^{2}+\frac{-6}{9}x+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{-6}{9} to lowest terms by extracting and canceling out 3.

$$\frac{7}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2+\frac{1}{27}x^{3}-\frac{1}{9}x^{2}-\frac{2}{3}x+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine \frac{7}{162}x^{3} and \frac{1}{27}x^{3} to get \frac{13}{162}x^{3}.

$$\frac{13}{162}x^{3}-\frac{5}{18}x^{2}-\frac{2}{9}x+2-\frac{1}{9}x^{2}-\frac{2}{3}x+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine -\frac{5}{18}x^{2} and -\frac{1}{9}x^{2} to get -\frac{7}{18}x^{2}.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{2}{9}x+2-\frac{2}{3}x+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Combine -\frac{2}{9}x and -\frac{2}{3}x to get -\frac{8}{9}x.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{10}{162}x\left(x+3\right)\left(x-3\right)$$

Reduce the fraction \frac{10}{162} to lowest terms by extracting and canceling out 2.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x\left(x+3\right)\left(x-3\right)$$

Use the distributive property to multiply \frac{5}{81}x by x+3.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\left(\frac{5}{81}xx+\frac{5}{81}x\times 3\right)\left(x-3\right)$$

Multiply x and x to get x^{2}.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\left(\frac{5}{81}x^{2}+\frac{5}{81}x\times 3\right)\left(x-3\right)$$

Express \frac{5}{81}\times 3 as a single fraction.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\left(\frac{5}{81}x^{2}+\frac{5\times 3}{81}x\right)\left(x-3\right)$$

Multiply 5 and 3 to get 15.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\left(\frac{5}{81}x^{2}+\frac{15}{81}x\right)\left(x-3\right)$$

Reduce the fraction \frac{15}{81} to lowest terms by extracting and canceling out 3.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\left(\frac{5}{81}x^{2}+\frac{5}{27}x\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of \frac{5}{81}x^{2}+\frac{5}{27}x by each term of x-3.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{2}x+\frac{5}{81}x^{2}\left(-3\right)+\frac{5}{27}xx+\frac{5}{27}x\left(-3\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}+\frac{5}{81}x^{2}\left(-3\right)+\frac{5}{27}xx+\frac{5}{27}x\left(-3\right)$$

Multiply x and x to get x^{2}.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}+\frac{5}{81}x^{2}\left(-3\right)+\frac{5}{27}x^{2}+\frac{5}{27}x\left(-3\right)$$

Express \frac{5}{81}\left(-3\right) as a single fraction.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}+\frac{5\left(-3\right)}{81}x^{2}+\frac{5}{27}x^{2}+\frac{5}{27}x\left(-3\right)$$

Multiply 5 and -3 to get -15.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}+\frac{-15}{81}x^{2}+\frac{5}{27}x^{2}+\frac{5}{27}x\left(-3\right)$$

Reduce the fraction \frac{-15}{81} to lowest terms by extracting and canceling out 3.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}-\frac{5}{27}x^{2}+\frac{5}{27}x^{2}+\frac{5}{27}x\left(-3\right)$$

Combine -\frac{5}{27}x^{2} and \frac{5}{27}x^{2} to get 0.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}+\frac{5}{27}x\left(-3\right)$$

Express \frac{5}{27}\left(-3\right) as a single fraction.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}+\frac{5\left(-3\right)}{27}x$$

Multiply 5 and -3 to get -15.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}+\frac{-15}{27}x$$

Reduce the fraction \frac{-15}{27} to lowest terms by extracting and canceling out 3.

$$\frac{13}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2+\frac{5}{81}x^{3}-\frac{5}{9}x$$

Combine \frac{13}{162}x^{3} and \frac{5}{81}x^{3} to get \frac{23}{162}x^{3}.

$$\frac{23}{162}x^{3}-\frac{7}{18}x^{2}-\frac{8}{9}x+2-\frac{5}{9}x$$

Combine -\frac{8}{9}x and -\frac{5}{9}x to get -\frac{13}{9}x.

$$\frac{23}{162}x^{3}-\frac{7}{18}x^{2}-\frac{13}{9}x+2$$