Question

Multiply the binomials: $\left(2pq+3q^2\right)$ and $\left(3pq-2q^2\right)$

Answer 1

Step 1: Follow the following steps to multiply two binomials.

• Apply distributive law of multiplication.
• Observe, that every term in one binomial multiplies every term in the other binomial.
• look for like terms, if any, and combine them.

Step 2: Multiply $\left(2pq+3q^2\right)$ and $\left(3pq-2q^2\right)$.

$\begin{array}{l}\left(2pq+3q^2\right)\times \left(3pq-2q^2\right)\\ =2pq\times \left(3pq-2q^2\right)+3q^2\times \left(3pq-2q^2\right)\\ =6p^2{q}^2-4p{q}^3+9p{q}^3-6q^4\\ =6p^2{q}^2+5p{q}^3-6q^4\end{array}$

Hence the product of $\left(2pq+3q^2\right)$ and $\left(3pq-2q^2\right)$ is $6p^2{q}^2+5p{q}^3-6q^4$.