Solve (p+q)^2+6(p+q)+9

$$( p + q ) ^ { 2 } + 6 ( p + q ) + 9$$

Evaluate

$$\left(p+q+3\right)^{2}$$

Solution Steps

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

$$p^{2}+2pq+q^{2}+6\left(p+q\right)+9$$

Use the distributive property to multiply 6 by p+q.

$$p^{2}+2pq+q^{2}+6p+6q+9$$

Expand

$$p^{2}+2pq+6p+q^{2}+6q+9$$

Solution Steps

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

$$p^{2}+2pq+q^{2}+6\left(p+q\right)+9$$

Use the distributive property to multiply 6 by p+q.

$$p^{2}+2pq+q^{2}+6p+6q+9$$