Solve (m+3)^2-n(2m+n+6)

$$( m + 3 ) ^ { 2 } - n ( 2 m + n + 6 )$$

Evaluate

$$-n\left(2m+n+6\right)+\left(m+3\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+3\right)^{2}.

$$m^{2}+6m+9-n\left(2m+n+6\right)$$

Use the distributive property to multiply n by 2m+n+6.

$$m^{2}+6m+9-\left(2nm+n^{2}+6n\right)$$

To find the opposite of 2nm+n^{2}+6n, find the opposite of each term.

$$m^{2}+6m+9-2nm-n^{2}-6n$$

Expand

$$m^{2}-2mn+6m-n^{2}-6n+9$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+3\right)^{2}.

$$m^{2}+6m+9-n\left(2m+n+6\right)$$

Use the distributive property to multiply n by 2m+n+6.

$$m^{2}+6m+9-\left(2nm+n^{2}+6n\right)$$

To find the opposite of 2nm+n^{2}+6n, find the opposite of each term.

$$m^{2}+6m+9-2nm-n^{2}-6n$$