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

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

Evaluate

$$2x^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

$$-4xy+2x\left(x+2y\right)$$

Use the distributive property to multiply 2x by x+2y.

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

Combine -4xy and 4xy to get 0.

$$2x^{2}$$

Expand

$$2x^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

$$-4xy+2x\left(x+2y\right)$$

Use the distributive property to multiply 2x by x+2y.

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

Combine -4xy and 4xy to get 0.

$$2x^{2}$$