Question

Evaluate: $(4a+3b{)}^2-(4a-3b{)}^2+48ab$.

• A. $76ab$
• B. $96ab$
• C. $46ab$
• D. $106ab$

Answer 1

The correct option is B $96ab$

Given, $(4a+3b{)}^2-(4a-3b{)}^2+48ab$.

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

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

Then,

$(4a+3b{)}^2-(4a-3b{)}^2+48ab$
$=\left(\right(4a{)}^2+2\left(4a\right)\left(3b\right)+\left(3b{)}^2\right)-\left(\right(4a{)}^2-2\left(4a\right)\left(3b\right)+\left(3b{)}^2\right)+48ab$
$=(4a{)}^2+2(4a\left)\right(3b)+(3b{)}^2-(4a{)}^2+2(4a\left)\right(3b)-(3b{)}^2+48ab$
$=24ab+24ab+48ab$

$=48ab+48ab$
$=96ab$.

Therefore, option $B$ is correct.