Solve (x-2)(x^2-6x)-x(x^2-2x-8)

$$( x - 2 ) ( x ^ { 2 } - 6 x ) - x ( x ^ { 2 } - 2 x - 8 )$$

Evaluate

$$2x\left(10-3x\right)$$

Solution Steps

Use the distributive property to multiply x-2 by x^{2}-6x and combine like terms.

$$x^{3}-8x^{2}+12x-x\left(x^{2}-2x-8\right)$$

Use the distributive property to multiply x by x^{2}-2x-8.

$$x^{3}-8x^{2}+12x-\left(x^{3}-2x^{2}-8x\right)$$

To find the opposite of x^{3}-2x^{2}-8x, find the opposite of each term.

$$x^{3}-8x^{2}+12x-x^{3}+2x^{2}+8x$$

Combine x^{3} and -x^{3} to get 0.

$$-8x^{2}+12x+2x^{2}+8x$$

Combine -8x^{2} and 2x^{2} to get -6x^{2}.

$$-6x^{2}+12x+8x$$

Combine 12x and 8x to get 20x.

$$-6x^{2}+20x$$

Expand

$$20x-6x^{2}$$

Solution Steps

Use the distributive property to multiply x-2 by x^{2}-6x and combine like terms.

$$x^{3}-8x^{2}+12x-x\left(x^{2}-2x-8\right)$$

Use the distributive property to multiply x by x^{2}-2x-8.

$$x^{3}-8x^{2}+12x-\left(x^{3}-2x^{2}-8x\right)$$

To find the opposite of x^{3}-2x^{2}-8x, find the opposite of each term.

$$x^{3}-8x^{2}+12x-x^{3}+2x^{2}+8x$$

Combine x^{3} and -x^{3} to get 0.

$$-8x^{2}+12x+2x^{2}+8x$$

Combine -8x^{2} and 2x^{2} to get -6x^{2}.

$$-6x^{2}+12x+8x$$

Combine 12x and 8x to get 20x.

$$-6x^{2}+20x$$