Question : Simplify the following expression.
$(3x+5)^2+(3x-5)^2$
Option 1: $500x$
Option 2: $450x$
Option 3: $9x^2+50$
Option 4: $2\left(9 x^2+25\right)$
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Correct Answer: $2\left(9 x^2+25\right)$
Solution :
Given: $(3x+5)^2+(3x-5)^2$
Expanding this expression by using algebraic identities, we have,
$=[(3x)^2+(5)^2+2×3x×5]+[(3x)^2+(5)^2–2×3x×5]$
$= [9x^2+25+30x+[9x^2+25–30x]$
$= 18x^2+50$
$= 2(9x^2+25)$
Hence, the correct answer is $2(9x^2+25)$.
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