Question

$\text{Factorise the expression:}{p}^2{q}^2+6pqr+9r^2$

• A. $(pq-3r)(3r-pq)$
• B. $(pq-3r)(pq-3r)$
• C. $(pq-3r)(pq+3r)$
• D. $(pq+3r)(pq+3r)$

Answer 1

The correct option is D $(pq+3r)(pq+3r)$

$\text{Given expression:}{p}^2{q}^2+6pqr+9r^2$

$\text{Above expression can be written as,}(pq{)}^2+2(pq\left)\right(3r)+(3r{)}^2$

$\text{Now, applying the identity}(a+b{)}^2=a^2+2ab+b^2,\text{we get,}$

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