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

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

Evaluate

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

Solution Steps

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

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

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

$$x^{2}-y^{2}+2yz-z^{2}$$

Expand

$$x^{2}-y^{2}+2yz-z^{2}$$

Solution Steps

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

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

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

$$x^{2}-y^{2}+2yz-z^{2}$$