Solve -left(x-mright)^2+m+2

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

Expand

$$2+m-m^{2}+2mx-x^{2}$$

Solution Steps

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

$$-\left(x^{2}-2xm+m^{2}\right)+m+2$$

To find the opposite of x^{2}-2xm+m^{2}, find the opposite of each term.

$$-x^{2}+2xm-m^{2}+m+2$$

Evaluate

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

Solution Steps

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

$$-\left(x^{2}-2xm+m^{2}\right)+m+2$$

To find the opposite of x^{2}-2xm+m^{2}, find the opposite of each term.

$$-x^{2}+2xm-m^{2}+m+2$$