Solve -1/3(x-1)(x-2)(x-3)

$$- \frac { 1 } { 3 } ( x - 1 ) ( x - 2 ) ( x - 3 )$$

Evaluate

$$-\frac{\left(x-3\right)\left(x-2\right)\left(x-1\right)}{3}$$

Solution Steps

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

$$\left(-\frac{1}{3}x-\frac{1}{3}\left(-1\right)\right)\left(x-2\right)\left(x-3\right)$$

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

$$\left(-\frac{1}{3}x+\frac{1}{3}\right)\left(x-2\right)\left(x-3\right)$$

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

$$\left(-\frac{1}{3}xx-\frac{1}{3}x\left(-2\right)+\frac{1}{3}x+\frac{1}{3}\left(-2\right)\right)\left(x-3\right)$$

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

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

Express -\frac{1}{3}\left(-2\right) as a single fraction.

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

Multiply -1 and -2 to get 2.

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

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

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

Multiply \frac{1}{3} and -2 to get \frac{-2}{3}.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

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

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

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

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

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

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

Multiply -1 and -3 to get 3.

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

Divide 3 by 3 to get 1.

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

Combine 1x^{2} and x^{2} to get 2x^{2}.

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

Combine -3x and -\frac{2}{3}x to get -\frac{11}{3}x.

$$-\frac{1}{3}x^{3}+2x^{2}-\frac{11}{3}x-\frac{2}{3}\left(-3\right)$$

Express -\frac{2}{3}\left(-3\right) as a single fraction.

$$-\frac{1}{3}x^{3}+2x^{2}-\frac{11}{3}x+\frac{-2\left(-3\right)}{3}$$

Multiply -2 and -3 to get 6.

$$-\frac{1}{3}x^{3}+2x^{2}-\frac{11}{3}x+\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$-\frac{1}{3}x^{3}+2x^{2}-\frac{11}{3}x+2$$

Expand

$$-\frac{x^{3}}{3}+2x^{2}-\frac{11x}{3}+2$$

Solution Steps

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

$$\left(-\frac{1}{3}x-\frac{1}{3}\left(-1\right)\right)\left(x-2\right)\left(x-3\right)$$

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

$$\left(-\frac{1}{3}x+\frac{1}{3}\right)\left(x-2\right)\left(x-3\right)$$

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

$$\left(-\frac{1}{3}xx-\frac{1}{3}x\left(-2\right)+\frac{1}{3}x+\frac{1}{3}\left(-2\right)\right)\left(x-3\right)$$

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

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

Express -\frac{1}{3}\left(-2\right) as a single fraction.

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

Multiply -1 and -2 to get 2.

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

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

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

Multiply \frac{1}{3} and -2 to get \frac{-2}{3}.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

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

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

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

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

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

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

Multiply -1 and -3 to get 3.

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

Divide 3 by 3 to get 1.

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

Combine 1x^{2} and x^{2} to get 2x^{2}.

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

Combine -3x and -\frac{2}{3}x to get -\frac{11}{3}x.

$$-\frac{1}{3}x^{3}+2x^{2}-\frac{11}{3}x-\frac{2}{3}\left(-3\right)$$

Express -\frac{2}{3}\left(-3\right) as a single fraction.

$$-\frac{1}{3}x^{3}+2x^{2}-\frac{11}{3}x+\frac{-2\left(-3\right)}{3}$$

Multiply -2 and -3 to get 6.

$$-\frac{1}{3}x^{3}+2x^{2}-\frac{11}{3}x+\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$-\frac{1}{3}x^{3}+2x^{2}-\frac{11}{3}x+2$$