Question

Simplify the expression:
$(3x+2{)}^2-(3x-2{)}^2$

• A. $x2+2x-4$
• B. $x2+24x$
• C. $24x+25$
• D. $24x$

Answer 1

The correct option is D $24x$

Given expression is
$(3x+2{)}^2-(3x-2{)}^2.$
Using the identity: $(a+b{)}^2=a^2+2ab+b^2$
and
$(a-b{)}^2=a^2-2ab+b^2,$
the above expression can be written as,
$(3x+2{)}^2-(3x-2{)}^2$
$=\left[\right(3x{)}^2+2\left(3x\right)\left(2\right)+\left(2{)}^2\right]-\left[\right(3x{)}^2-2\left(3x\right)\left(2\right)+\left(2{)}^2\right]$
$=\left[\right(9x^2+12x+4)-(9x^2-12x+4\left)\right]$
$=9x^2-9x^2+12x+12x+4-4$
$=24x$