Question

Factorise the following expression.

$63p^2{q}^2{r}^{2}s-9p{q}^2{r}^2{s}^2+15p^{2}q{r}^2{s}^2-60p^2{q}^{2}r{s}^2$

Answer 1

We have, $63p^2{q}^2{r}^{2}s-9p{q}^2{r}^2{s}^2+15p^{2}q{r}^2{s}^2-60p^2{q}^{2}r{s}^2$
$=3\times 21p^2{q}^2{r}^{2}s-3\times 3p{q}^2{r}^2{s}^2+3\times 5p^{2}q{r}^2{s}^2-3\times 20p^2{q}^{2}r{s}^2$
$=3pqrs(21pqr-3qrs+5prs-20pqs)$