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

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

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.

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