Question

Factorize the following algebraic expression:

$p^2{q}^2-6pqr+9r^2$

Answer 1

Given $p^2{q}^2-6pqr+9r^2$

$=(pq{)}^2-2(pq\left)\right(3r)+(3r{)}^2$

Using the formula, $(x-y{)}^2=x^2-2xy+y^2$

$=(pq-3r{)}^2$

$=(pq-3r)(pq-3r)$

$\therefore p^2{q}^2-6pqr+9r^2=(pq-3r)(pq-3r)$