Solve (x-4)^2-x(2x-1)

$$( x - 4 ) ^ { 2 } - x ( 2 x - 1 )$$

Evaluate

$$16-7x-x^{2}$$

Solution Steps

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

$$x^{2}-8x+16-x\left(2x-1\right)$$

Use the distributive property to multiply x by 2x-1.

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

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

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

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

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

Combine -8x and x to get -7x.

$$-x^{2}-7x+16$$

Expand

$$16-7x-x^{2}$$

Solution Steps

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

$$x^{2}-8x+16-x\left(2x-1\right)$$

Use the distributive property to multiply x by 2x-1.

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

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

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

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

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

Combine -8x and x to get -7x.

$$-x^{2}-7x+16$$