Solve 1/4((x+y)^2-(x-y)^2)

$$\frac { 1 } { 4 } ( ( x + y ) ^ { 2 } - ( x - y ) ^ { 2 } )$$

Evaluate

$$xy$$

Solution Steps

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

$$\frac{1}{4}\left(x^{2}+2xy+y^{2}-\left(x-y\right)^{2}\right)$$

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

$$\frac{1}{4}\left(x^{2}+2xy+y^{2}-\left(x^{2}-2xy+y^{2}\right)\right)$$

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

$$\frac{1}{4}\left(x^{2}+2xy+y^{2}-x^{2}+2xy-y^{2}\right)$$

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

$$\frac{1}{4}\left(2xy+y^{2}+2xy-y^{2}\right)$$

Combine 2xy and 2xy to get 4xy.

$$\frac{1}{4}\left(4xy+y^{2}-y^{2}\right)$$

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

$$\frac{1}{4}\times 4xy$$

Multiply \frac{1}{4} and 4 to get 1.

$$xy$$

Expand

$$xy$$

Solution Steps

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

$$\frac{1}{4}\left(x^{2}+2xy+y^{2}-\left(x-y\right)^{2}\right)$$

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

$$\frac{1}{4}\left(x^{2}+2xy+y^{2}-\left(x^{2}-2xy+y^{2}\right)\right)$$

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

$$\frac{1}{4}\left(x^{2}+2xy+y^{2}-x^{2}+2xy-y^{2}\right)$$

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

$$\frac{1}{4}\left(2xy+y^{2}+2xy-y^{2}\right)$$

Combine 2xy and 2xy to get 4xy.

$$\frac{1}{4}\left(4xy+y^{2}-y^{2}\right)$$

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

$$\frac{1}{4}\times 4xy$$

Multiply \frac{1}{4} and 4 to get 1.

$$xy$$