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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

Expand

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

Solution Steps

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

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

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

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

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

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