Which of the following is equal to $(2 x + 3 y)^{2}$ ?

4 x^{2} + 9 y^{2}

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4 x^{2} + 12 x y + 9 y^{2}

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4 x^{2} - 12 x y + 9 y^{2}

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4 x^{2} + 6 x y + 9 y^{2}

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Solution

The correct option is B $4 x^{2} + 12 x y + 9 y^{2}$
We know $(x + y)^{2}$ = $x^{2} + 2 x y + y^{2}$
Comparing we get x = 2x and y = 3y
$\Rightarrow$ ( $2 x + 3 y)^{2}$ = $(2 x)^{2} + 2 (2 x) (3 y) + (3 y)^{2}$
$\Rightarrow$ $4 x^{2} + 12 x y + 9 y^{2}$

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