Question

Factorise the expression and divide them as directed: $5pq\left(p^2-q^2\right)÷2p\left(p+q\right)$.

Answer 1

Step 1: Factorize the expression $5pq\left(p^2-q^2\right)$.

Using identity $a^2-b^2=\left(a+b\right)\left(a-b\right)$, expand the above expression.

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

Step 2: Divide the above expression by $2p\left(p+q\right)$ to get the final answer.

$\Rightarrow \frac{5pq\left(p+q\right)\left(p-q\right)}{2p\left(p+q\right)}=\frac{5}{2}q\left(p-q\right)$

Hence, the required final answer is $\frac{5}{2}q\left(p-q\right)$.