Solve (m+n)^2-6(m+n)+0

$$( m + n ) ^ { 2 } - 6 ( m + n ) + 0$$

Evaluate

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

Solution Steps

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

$$m^{2}+2mn+n^{2}-6\left(m+n\right)+0$$

Use the distributive property to multiply -6 by m+n.

$$m^{2}+2mn+n^{2}-6m-6n+0$$

Anything plus zero gives itself.

$$m^{2}+2mn+n^{2}-6m-6n$$

Expand

$$m^{2}+2mn-6m+n^{2}-6n$$

Solution Steps

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

$$m^{2}+2mn+n^{2}-6\left(m+n\right)+0$$

Use the distributive property to multiply -6 by m+n.

$$m^{2}+2mn+n^{2}-6m-6n+0$$

Anything plus zero gives itself.

$$m^{2}+2mn+n^{2}-6m-6n$$