Solve left(x-4right)^2-left(x-2right)left(x-8right)

$${ \left(x-4 \right) }^{ 2 } - \left( x-2 \right) \left( x-8 \right)$$

Evaluate

$$2x$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$x^{2}-8x+16-\left(x-2\right)\left(x-8\right)$$

Use the distributive property to multiply x-2 by x-8 and combine like terms.

$$x^{2}-8x+16-\left(x^{2}-10x+16\right)$$

To find the opposite of x^{2}-10x+16, find the opposite of each term.

$$x^{2}-8x+16-x^{2}+10x-16$$

Combine x^{2} and -x^{2} to get 0.

$$-8x+16+10x-16$$

Combine -8x and 10x to get 2x.

$$2x+16-16$$

Subtract 16 from 16 to get 0.

$$2x$$

Expand

$$2x$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$x^{2}-8x+16-\left(x-2\right)\left(x-8\right)$$

Use the distributive property to multiply x-2 by x-8 and combine like terms.

$$x^{2}-8x+16-\left(x^{2}-10x+16\right)$$

To find the opposite of x^{2}-10x+16, find the opposite of each term.

$$x^{2}-8x+16-x^{2}+10x-16$$

Combine x^{2} and -x^{2} to get 0.

$$-8x+16+10x-16$$

Combine -8x and 10x to get 2x.

$$2x+16-16$$

Subtract 16 from 16 to get 0.

$$2x$$