Solve (x-y)^2-(x+y)^2=

$$( x - y ) ^ { 2 } - ( x + y ) ^ { 2 } =$$

Evaluate

$$-4xy$$

Solution Steps

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

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

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

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

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

$$x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}$$

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

$$-2xy+y^{2}-2xy-y^{2}$$

Combine -2xy and -2xy to get -4xy.

$$-4xy+y^{2}-y^{2}$$

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

$$-4xy$$

Expand

$$-4xy$$

Solution Steps

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

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

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

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

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

$$x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}$$

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

$$-2xy+y^{2}-2xy-y^{2}$$

Combine -2xy and -2xy to get -4xy.

$$-4xy+y^{2}-y^{2}$$

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

$$-4xy$$