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

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

Evaluate

$$-16x$$

Solution Steps

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

$$x^{2}-8x+16-\left(x+4\right)^{2}$$

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

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

To find the opposite of x^{2}+8x+16, find the opposite of each term.

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

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

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

Combine -8x and -8x to get -16x.

$$-16x+16-16$$

Subtract 16 from 16 to get 0.

$$-16x$$

Expand

$$-16x$$

Solution Steps

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

$$x^{2}-8x+16-\left(x+4\right)^{2}$$

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

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

To find the opposite of x^{2}+8x+16, find the opposite of each term.

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

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

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

Combine -8x and -8x to get -16x.

$$-16x+16-16$$

Subtract 16 from 16 to get 0.

$$-16x$$