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

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

Evaluate

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

Solution Steps

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

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

To find the opposite of 4y^{2}-4yp+p^{2}, find the opposite of each term.

$$x^{2}-4y^{2}+4yp-p^{2}$$

Expand

$$x^{2}-4y^{2}+4py-p^{2}$$

Solution Steps

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

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

To find the opposite of 4y^{2}-4yp+p^{2}, find the opposite of each term.

$$x^{2}-4y^{2}+4yp-p^{2}$$