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

4 x^{2} + 24 x y - 15 y^{2}

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4 x^{2} + 16 x y + 25 y^{2}

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

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

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Solution

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

We know, $(x + a) (x + b) = x^{2} + (a + b) x + a b$ .

On comparing, we get,
$x = 2 x, a = 5 y, b = 3 y$ .

Thus,
$(2 x + 5 y) (2 x + 3 y)$
$= (2 x)^{2} + (5 y + 3 y) 2 x + (5 y) \times (3 y)$
$= 4 x^{2} + (8 y) 2 x + 15 y^{2}$
$= 4 x^{2} + 16 x y + 15 y^{2}$ .

Hence, option $C$ is correct.

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