Question

Find the missing expression:
${(4pq+3q)}^2-{(4pq-3q)}^2=$ _________.

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

Answer 1

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

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

We have:

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

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

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

$=24p{q}^2+24p{q}^2$
$=48p{q}^2$