Question

Find the value of ${(4pq+3q)}^2-{(4pq-3q)}^2$.

Answer 1

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

We have:

$(a+b{)}^2=a^2+2ab+b^2(a-b{)}^2=a^2-2ab+b^2$
[1 mark]
So, ${(4pq+3q)}^2-{(4pq-3q)}^2$

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