Solve (3m+n)^2-8(3m+n)+16

$$( 3 m + n ) ^ { 2 } - 8 ( 3 m + n ) + 16$$

Evaluate

$$\left(3m+n-4\right)^{2}$$

Solution Steps

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

$$9m^{2}+6mn+n^{2}-8\left(3m+n\right)+16$$

Use the distributive property to multiply -8 by 3m+n.

$$9m^{2}+6mn+n^{2}-24m-8n+16$$

Expand

$$9m^{2}+6mn-24m+n^{2}-8n+16$$

Solution Steps

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

$$9m^{2}+6mn+n^{2}-8\left(3m+n\right)+16$$

Use the distributive property to multiply -8 by 3m+n.

$$9m^{2}+6mn+n^{2}-24m-8n+16$$