The value of $(x + 3 y)^{2} + (x - 3 y)^{2}$ is:

2 x^{2} + 18 y^{2}

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2 x^{2} - 18 y^{2}

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2 x^{2} + 18 y^{2} - 2 x y

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None of these

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Solution

The correct option is A $2 x^{2} + 18 y^{2}$
We know, $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ and $(a - b)^{2} = a^{2} - 2 a b + b^{2}$ .

Then,
$(x + 3 y)^{2} + (x - 3 y)^{2} = [(x)^{2} + (3 y)^{2} + 2 \times x \times 3 y] + [(x)^{2} + (3 y)^{2} - 2 \times x \times 3 y]$
$= x^{2} + 9 y^{2} + 6 x y + x^{2} + 9 y^{2} - 6 x y$
$= 2 x^{2} + 18 y^{2}$ .

Hence, Option $A$ is correct.

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