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

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

Evaluate

$$x\left(1+2y-x\right)$$

Solution Steps

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

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

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

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

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

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

Expand

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

Solution Steps

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

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

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

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

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

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