Solve (-5x+6x+3/2x)(-2a+8a)(1/3x-x)-3x(2ax-44/9ax)

$$( - 5 x + 6 x + \frac { 3 } { 2 } x ) ( - 2 a + 8 a ) ( \frac { 1 } { 3 } x - x ) - 3 x ( 2 a x - \frac { 44 } { 9 } a x )$$

Evaluate

$$-\frac{4ax^{2}}{3}$$

Solution Steps

Combine -5x and 6x to get x.

$$\left(x+\frac{3}{2}x\right)\left(-2a+8a\right)\left(\frac{1}{3}x-x\right)-3x\left(2ax-\frac{44}{9}ax\right)$$

Combine x and \frac{3}{2}x to get \frac{5}{2}x.

$$\frac{5}{2}x\left(-2a+8a\right)\left(\frac{1}{3}x-x\right)-3x\left(2ax-\frac{44}{9}ax\right)$$

Combine -2a and 8a to get 6a.

$$\frac{5}{2}x\times 6a\left(\frac{1}{3}x-x\right)-3x\left(2ax-\frac{44}{9}ax\right)$$

Express \frac{5}{2}\times 6 as a single fraction.

$$\frac{5\times 6}{2}xa\left(\frac{1}{3}x-x\right)-3x\left(2ax-\frac{44}{9}ax\right)$$

Multiply 5 and 6 to get 30.

$$\frac{30}{2}xa\left(\frac{1}{3}x-x\right)-3x\left(2ax-\frac{44}{9}ax\right)$$

Divide 30 by 2 to get 15.

$$15xa\left(\frac{1}{3}x-x\right)-3x\left(2ax-\frac{44}{9}ax\right)$$

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

$$15xa\left(-\frac{2}{3}\right)x-3x\left(2ax-\frac{44}{9}ax\right)$$

Express 15\left(-\frac{2}{3}\right) as a single fraction.

$$\frac{15\left(-2\right)}{3}xax-3x\left(2ax-\frac{44}{9}ax\right)$$

Multiply 15 and -2 to get -30.

$$\frac{-30}{3}xax-3x\left(2ax-\frac{44}{9}ax\right)$$

Divide -30 by 3 to get -10.

$$-10xax-3x\left(2ax-\frac{44}{9}ax\right)$$

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

$$-10x^{2}a-3x\left(2ax-\frac{44}{9}ax\right)$$

Combine 2ax and -\frac{44}{9}ax to get -\frac{26}{9}ax.

$$-10x^{2}a-3x\left(-\frac{26}{9}\right)ax$$

Express 3\left(-\frac{26}{9}\right) as a single fraction.

$$-10x^{2}a-\frac{3\left(-26\right)}{9}xax$$

Multiply 3 and -26 to get -78.

$$-10x^{2}a-\frac{-78}{9}xax$$

Reduce the fraction \frac{-78}{9} to lowest terms by extracting and canceling out 3.

$$-10x^{2}a-\left(-\frac{26}{3}xax\right)$$

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

$$-10x^{2}a-\left(-\frac{26}{3}x^{2}a\right)$$

The opposite of -\frac{26}{3}x^{2}a is \frac{26}{3}x^{2}a.

$$-10x^{2}a+\frac{26}{3}x^{2}a$$

Combine -10x^{2}a and \frac{26}{3}x^{2}a to get -\frac{4}{3}x^{2}a.

$$-\frac{4}{3}x^{2}a$$

Expand

$$-\frac{4ax^{2}}{3}$$

Solution Steps

Combine -5x and 6x to get x.

$$\left(x+\frac{3}{2}x\right)\left(-2a+8a\right)\left(\frac{1}{3}x-x\right)-3x\left(2ax-\frac{44}{9}ax\right)$$

Combine x and \frac{3}{2}x to get \frac{5}{2}x.

$$\frac{5}{2}x\left(-2a+8a\right)\left(\frac{1}{3}x-x\right)-3x\left(2ax-\frac{44}{9}ax\right)$$

Combine -2a and 8a to get 6a.

$$\frac{5}{2}x\times 6a\left(\frac{1}{3}x-x\right)-3x\left(2ax-\frac{44}{9}ax\right)$$

Express \frac{5}{2}\times 6 as a single fraction.

$$\frac{5\times 6}{2}xa\left(\frac{1}{3}x-x\right)-3x\left(2ax-\frac{44}{9}ax\right)$$

Multiply 5 and 6 to get 30.

$$\frac{30}{2}xa\left(\frac{1}{3}x-x\right)-3x\left(2ax-\frac{44}{9}ax\right)$$

Divide 30 by 2 to get 15.

$$15xa\left(\frac{1}{3}x-x\right)-3x\left(2ax-\frac{44}{9}ax\right)$$

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

$$15xa\left(-\frac{2}{3}\right)x-3x\left(2ax-\frac{44}{9}ax\right)$$

Express 15\left(-\frac{2}{3}\right) as a single fraction.

$$\frac{15\left(-2\right)}{3}xax-3x\left(2ax-\frac{44}{9}ax\right)$$

Multiply 15 and -2 to get -30.

$$\frac{-30}{3}xax-3x\left(2ax-\frac{44}{9}ax\right)$$

Divide -30 by 3 to get -10.

$$-10xax-3x\left(2ax-\frac{44}{9}ax\right)$$

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

$$-10x^{2}a-3x\left(2ax-\frac{44}{9}ax\right)$$

Combine 2ax and -\frac{44}{9}ax to get -\frac{26}{9}ax.

$$-10x^{2}a-3x\left(-\frac{26}{9}\right)ax$$

Express 3\left(-\frac{26}{9}\right) as a single fraction.

$$-10x^{2}a-\frac{3\left(-26\right)}{9}xax$$

Multiply 3 and -26 to get -78.

$$-10x^{2}a-\frac{-78}{9}xax$$

Reduce the fraction \frac{-78}{9} to lowest terms by extracting and canceling out 3.

$$-10x^{2}a-\left(-\frac{26}{3}xax\right)$$

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

$$-10x^{2}a-\left(-\frac{26}{3}x^{2}a\right)$$

The opposite of -\frac{26}{3}x^{2}a is \frac{26}{3}x^{2}a.

$$-10x^{2}a+\frac{26}{3}x^{2}a$$

Combine -10x^{2}a and \frac{26}{3}x^{2}a to get -\frac{4}{3}x^{2}a.

$$-\frac{4}{3}x^{2}a$$