Expand $(2 x + 4 y)^{2}$ using algebraic identity.

x^{2} + 8 x y + 16 y^{2}

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4 x^{2} + 16 x y + 16 y^{2}

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2 x^{2} + 8 x y + 4 y^{2}

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

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Solution

The correct option is B $4 x^{2} + 16 x y + 16 y^{2}$
We know
$(x + y)^{2} = x^{2} + 2 x y + y^{2}$
Comparing the given expression with $(x + y)^{2}$ , we have
$x = 2 x, y = 4 y$
$(2 x + 4 y)^{2} = (2 x)^{2} + 2 (2 x) (4 y) + (4 y)^{2}$
$\Rightarrow 4 x^{2} + 16 x y + 16 y^{2}$

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