Solve x^2-(1+y)^2

$$x ^ { 2 } - ( 1 + y ) ^ { 2 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+y\right)^{2}.

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

To find the opposite of 1+2y+y^{2}, find the opposite of each term.

$$x^{2}-1-2y-y^{2}$$

Expand

$$x^{2}-y^{2}-2y-1$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+y\right)^{2}.

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

To find the opposite of 1+2y+y^{2}, find the opposite of each term.

$$x^{2}-1-2y-y^{2}$$