Question

(4pq+3q)2−(4pq−3q)2 =

• A. $44p{q}^2$
• B. $48p^{2}q$
• C. $48p{q}^2$
• D. $44p^{2}q$

Answer 1

The correct option is C $48p{q}^2$

By applying $(a+b{)}^2=a^2+2ab+b^2,$ and $(a-b{)}^2=a^2-2ab+b^2$ in the given expression, we get,

${(4pq+3q)}^2-{(4pq-3q)}^2$
$=[{\left(4pq\right)}^2+{\left(3q\right)}^2+2(4pq\left)\right(3q\left)\right]$
$-[{\left(4pq\right)}^2+{\left(3q\right)}^2-2(4pq\left)\right(3q\left)\right]$
On simplifying, we get,
$=24p{q}^2+24p{q}^2$
$=48p{q}^2$