Question

Factorize the following expression:

$p^2{q}^2-p^4{q}^4$

Answer 1

Given: $p^2{q}^2-p^4{q}^4$

$\therefore p^2{q}^2-p^4{q}^4$
$=p^2{q}^2(1-p^2{q}^2)$
$=p^2{q}^2\left[\right(1{)}^2-\left(pq{)}^2\right]$

Using the fomula , $(a^2-b^2)=(a-b)(a+b)$

$=p^2{q}^2(1+pq)(1-pq)$

Hence, $p^2{q}^2-p^4{q}^4=p^2{q}^2(1+pq)(1-pq)$