Solve 4a^2-(x+y)^2

$$4 a ^ { 2 } - ( x + y ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

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

$$4a^{2}-x^{2}-2xy-y^{2}$$

Expand

$$4a^{2}-y^{2}-2xy-x^{2}$$

Solution Steps

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

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

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

$$4a^{2}-x^{2}-2xy-y^{2}$$