Question

Factories the given algebraic expression by taking out the common terms. Also, write the common term
$5pq+20p^3{q}^3-15p^{2}q$

Answer 1

We first factorize each term of the given expression $5pq+20p^3{q}^3-15p^{2}q$ as shown below:

$5pq=5\times p\times q20p^3{q}^3=2\times 2\times 5\times p\times p\times p\times q\times q\times q15p^{2}q=3\times 5\times p\times p\times q$

The common factors are $5,p$ and $q$, therefore, the HCF is $5\times p\times q=5pq$.

Now, by taking out the common term(HCF), we have:

$5pq+20p^3{q}^3-15p^{2}q=5pq(1+4p^2{q}^2-3p)$

Hence, the common term is $5pq$.