Solve 8+6(p+q)-5(p+q)^2

$$8 + 6 ( p + q ) - 5 ( p + q ) ^ { 2 }$$

Evaluate

$$-5\left(p+q\right)^{2}+6p+6q+8$$

Solution Steps

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

$$8+6p+6q-5\left(p+q\right)^{2}$$

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

$$8+6p+6q-5\left(p^{2}+2pq+q^{2}\right)$$

Use the distributive property to multiply -5 by p^{2}+2pq+q^{2}.

$$8+6p+6q-5p^{2}-10pq-5q^{2}$$

Expand

$$8+6q-5q^{2}+6p-10pq-5p^{2}$$

Solution Steps

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

$$8+6p+6q-5\left(p+q\right)^{2}$$

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

$$8+6p+6q-5\left(p^{2}+2pq+q^{2}\right)$$

Use the distributive property to multiply -5 by p^{2}+2pq+q^{2}.

$$8+6p+6q-5p^{2}-10pq-5q^{2}$$