Solve {l}{(-m+6)^2}{-(m-6)^2}

$$\left. \begin{array} { l } { ( - m + 6 ) ^ { 2 } } \\ { - ( m - 6 ) ^ { 2 } } \end{array} \right.$$

Evaluate

$$0$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-m+6\right)^{2}.

$$\left(-m\right)^{2}+12\left(-m\right)+36-\left(m-6\right)^{2}$$

Calculate -m to the power of 2 and get m^{2}.

$$m^{2}+12\left(-m\right)+36-\left(m-6\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m-6\right)^{2}.

$$m^{2}+12\left(-m\right)+36-\left(m^{2}-12m+36\right)$$

To find the opposite of m^{2}-12m+36, find the opposite of each term.

$$m^{2}+12\left(-m\right)+36-m^{2}+12m-36$$

Combine m^{2} and -m^{2} to get 0.

$$12\left(-m\right)+36+12m-36$$

Subtract 36 from 36 to get 0.

$$12\left(-m\right)+12m$$

Multiply 12 and -1 to get -12.

$$-12m+12m$$

Combine -12m and 12m to get 0.

$$0$$

Factor

$$0$$

Solution Steps

The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$0$$

Consider -2m+12. Factor out 2.

$$2\left(-m+6\right)$$

Rewrite the complete factored expression. Simplify.

$$0$$