Solve -xleft(x-3right)left(x-2right)/16*6

$$- \frac{ x \left( x-3 \right) \left( x-2 \right) }{ 16 } \times 6$$

Evaluate

$$-\frac{3x\left(x-3\right)\left(x-2\right)}{8}$$

Solution Steps

Use the distributive property to multiply x by x-3.

$$\left(-\frac{\left(x^{2}-3x\right)\left(x-2\right)}{16}\right)\times 6$$

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

$$\left(-\frac{x^{3}-2x^{2}-3x^{2}+6x}{16}\right)\times 6$$

Combine -2x^{2} and -3x^{2} to get -5x^{2}.

$$\left(-\frac{x^{3}-5x^{2}+6x}{16}\right)\times 6$$

Express \left(-\frac{x^{3}-5x^{2}+6x}{16}\right)\times 6 as a single fraction.

$$\frac{-\left(x^{3}-5x^{2}+6x\right)\times 6}{16}$$

Multiply -1 and 6 to get -6.

$$\frac{-6\left(x^{3}-5x^{2}+6x\right)}{16}$$

Divide -6\left(x^{3}-5x^{2}+6x\right) by 16 to get -\frac{3}{8}\left(x^{3}-5x^{2}+6x\right).

$$-\frac{3}{8}\left(x^{3}-5x^{2}+6x\right)$$

Use the distributive property to multiply -\frac{3}{8} by x^{3}-5x^{2}+6x.

$$-\frac{3}{8}x^{3}-\frac{3}{8}\left(-5\right)x^{2}-\frac{3}{8}\times 6x$$

Express -\frac{3}{8}\left(-5\right) as a single fraction.

$$-\frac{3}{8}x^{3}+\frac{-3\left(-5\right)}{8}x^{2}-\frac{3}{8}\times 6x$$

Multiply -3 and -5 to get 15.

$$-\frac{3}{8}x^{3}+\frac{15}{8}x^{2}-\frac{3}{8}\times 6x$$

Express -\frac{3}{8}\times 6 as a single fraction.

$$-\frac{3}{8}x^{3}+\frac{15}{8}x^{2}+\frac{-3\times 6}{8}x$$

Multiply -3 and 6 to get -18.

$$-\frac{3}{8}x^{3}+\frac{15}{8}x^{2}+\frac{-18}{8}x$$

Reduce the fraction \frac{-18}{8} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{8}x^{3}+\frac{15}{8}x^{2}-\frac{9}{4}x$$

Expand

$$-\frac{3x^{3}}{8}+\frac{15x^{2}}{8}-\frac{9x}{4}$$

Solution Steps

Use the distributive property to multiply x by x-3.

$$\left(-\frac{\left(x^{2}-3x\right)\left(x-2\right)}{16}\right)\times 6$$

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

$$\left(-\frac{x^{3}-2x^{2}-3x^{2}+6x}{16}\right)\times 6$$

Combine -2x^{2} and -3x^{2} to get -5x^{2}.

$$\left(-\frac{x^{3}-5x^{2}+6x}{16}\right)\times 6$$

Express \left(-\frac{x^{3}-5x^{2}+6x}{16}\right)\times 6 as a single fraction.

$$\frac{-\left(x^{3}-5x^{2}+6x\right)\times 6}{16}$$

Multiply -1 and 6 to get -6.

$$\frac{-6\left(x^{3}-5x^{2}+6x\right)}{16}$$

Divide -6\left(x^{3}-5x^{2}+6x\right) by 16 to get -\frac{3}{8}\left(x^{3}-5x^{2}+6x\right).

$$-\frac{3}{8}\left(x^{3}-5x^{2}+6x\right)$$

Use the distributive property to multiply -\frac{3}{8} by x^{3}-5x^{2}+6x.

$$-\frac{3}{8}x^{3}-\frac{3}{8}\left(-5\right)x^{2}-\frac{3}{8}\times 6x$$

Express -\frac{3}{8}\left(-5\right) as a single fraction.

$$-\frac{3}{8}x^{3}+\frac{-3\left(-5\right)}{8}x^{2}-\frac{3}{8}\times 6x$$

Multiply -3 and -5 to get 15.

$$-\frac{3}{8}x^{3}+\frac{15}{8}x^{2}-\frac{3}{8}\times 6x$$

Express -\frac{3}{8}\times 6 as a single fraction.

$$-\frac{3}{8}x^{3}+\frac{15}{8}x^{2}+\frac{-3\times 6}{8}x$$

Multiply -3 and 6 to get -18.

$$-\frac{3}{8}x^{3}+\frac{15}{8}x^{2}+\frac{-18}{8}x$$

Reduce the fraction \frac{-18}{8} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{8}x^{3}+\frac{15}{8}x^{2}-\frac{9}{4}x$$