Solve 6(p+q)^2+11(p+q)-10

$$6 ( p + q ) ^ { 2 } + 11 ( p + q ) - 10$$

Evaluate

$$6\left(p+q\right)^{2}+11p+11q-10$$

Solution Steps

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

$$6\left(p^{2}+2pq+q^{2}\right)+11\left(p+q\right)-10$$

Use the distributive property to multiply 6 by p^{2}+2pq+q^{2}.

$$6p^{2}+12pq+6q^{2}+11\left(p+q\right)-10$$

Use the distributive property to multiply 11 by p+q.

$$6p^{2}+12pq+6q^{2}+11p+11q-10$$

Expand

$$6p^{2}+12pq+11p+6q^{2}+11q-10$$

Solution Steps

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

$$6\left(p^{2}+2pq+q^{2}\right)+11\left(p+q\right)-10$$

Use the distributive property to multiply 6 by p^{2}+2pq+q^{2}.

$$6p^{2}+12pq+6q^{2}+11\left(p+q\right)-10$$

Use the distributive property to multiply 11 by p+q.

$$6p^{2}+12pq+6q^{2}+11p+11q-10$$