Question : Simplify $(3 x+2 y)^2-(3 x-2 y)^2$.
Option 1: $12 x y$
Option 2: $18 x^2-8 y^2$
Option 3: $24 xy$
Option 4: $9x^2-4y^2$
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Correct Answer: $24 xy$
Solution :
$(3x+2y)^2-(3x−2y)^2$
$=[(3x)^2+(2y)^2+2(3x)(2y)]-[(3x)^2+(2y)^2−2(3x)(2y)]$
$=[9x^2+4y^2+12xy]-[9x^2+4y^2−12xy]$
$=9x^2+4y^2+12xy-9x^2-4y^2+12xy$
$=24xy$
Hence, the correct answer is $24xy$.
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