Question

${(4pq+3q)}^2-{(4pq-3q)}^2=$ ___.

• A. 44p
• B. 48q
• C. 48pq²
• D. 44q

Answer 1

The correct option is C

48pq²

Given, ${(4pq+3q)}^2-{(4pq-3q)}^2$

We know
$(a+b{)}^2=a^2+2ab+b^2$
$and(a-b{)}^2=a^2-2ab+b^2$

Applying these two identities, we can write tha above equation as
$=[{\left(4pq\right)}^2+{\left(3q\right)}^2+2(4pq\left)\right(3q\left)\right]-[{\left(4pq\right)}^2+{\left(3q\right)}^2-2(4pq\left)\right(3q\left)\right]$

$=\left[\right(4pq{)}^2-\left(4pq{)}^2\right)+(3q^2-3q^2)+(24p{q}^2+24p{q}^2)$
$=24p{q}^2+24p{q}^2=48p{q}^2$