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

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

Evaluate

$$4hx$$

Solution Steps

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

$$x^{2}+2xh+h^{2}-\left(x-h\right)^{2}$$

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

$$x^{2}+2xh+h^{2}-\left(x^{2}-2xh+h^{2}\right)$$

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

$$x^{2}+2xh+h^{2}-x^{2}+2xh-h^{2}$$

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

$$2xh+h^{2}+2xh-h^{2}$$

Combine 2xh and 2xh to get 4xh.

$$4xh+h^{2}-h^{2}$$

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

$$4xh$$

Expand

$$4hx$$

Solution Steps

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

$$x^{2}+2xh+h^{2}-\left(x-h\right)^{2}$$

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

$$x^{2}+2xh+h^{2}-\left(x^{2}-2xh+h^{2}\right)$$

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

$$x^{2}+2xh+h^{2}-x^{2}+2xh-h^{2}$$

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

$$2xh+h^{2}+2xh-h^{2}$$

Combine 2xh and 2xh to get 4xh.

$$4xh+h^{2}-h^{2}$$

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

$$4xh$$