Question

What is the product of 2p + q and -3q - 6p + 1

Answer 1

`\large\boxed{(2p+q)(-3q-6p+1)=-3q^2-12p^2-12pq+2p+q}`

Explanation:

Use the distributive property: a(b + c) = ab + ac

`(2p+q)(-3q-6p+1)=(2p+q)(-3q)+(2p+q)(-6p)+(2p+q)(1)\\\\=(2p)(-3q)+(q)(-3q)+(2p)(-6p)+(q)(-6p)+2p+q\\\\=-6pq-3q^2-12p^2-6pq+2p+q\qquad\text{combine like terms}\\\\=-3q^2-12p^2+(-6pq-6pq)+2p+q=-3q^2-12p^2-12pq+2p+q`