Use the identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$ to find the following product.
$(2 x + 5 y) (2 x + 3 y)$

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

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4 x^{2} + 16 x y - 15 y^{2}

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4 x^{2} - 16 x y + 15 y^{2}

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4 x^{2} + 16 x y + 15 y^{2}

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Solution

The correct option is D $4 x^{2} + 16 x y + 15 y^{2}$
Given: $(2 x + 5 y) (2 x + 3 y)$

Using, $(x + a) (x + b) = x^{2} + (a + b) x + a b$ we get,

$= 4 x^{2} + (5 y + 3 y) 2 x + (5 y) (3 y)$

$= 4 x^{2} + 16 x y + 15 y^{2}$

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