Solve [(x+y)^2-(x-y)^2]^2

$$[ ( x + y ) ^ { 2 } - ( x - y ) ^ { 2 } ] ^ { 2 }$$

Evaluate

$$16\left(xy\right)^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

Combine 2xy and 2xy to get 4xy.

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

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

$$\left(4xy\right)^{2}$$

Expand \left(4xy\right)^{2}.

$$4^{2}x^{2}y^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}y^{2}$$

Expand

$$16\left(xy\right)^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

Combine 2xy and 2xy to get 4xy.

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

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

$$\left(4xy\right)^{2}$$

Expand \left(4xy\right)^{2}.

$$4^{2}x^{2}y^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}y^{2}$$