Use the identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$ to find the given product:
$(2 a^{2} + 9)$ $(2 a^{2} + 5)$ .

4 a^{4} + 28 a^{2} - 5

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4 a^{4} + 28 a^{2} + 45

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4 a^{3} + 28 a^{2} + 45

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a^{4} + 28 a^{2} + 45

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Solution

The correct option is B $4 a^{4} + 28 a^{2} + 45$
Given, $(2 a^{2} + 9) (2 a^{2} + 5)$ .

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

On comparing, we get,
$x = 2 a^{2}, a = 9, b = 5$ .

Thus,
$(2 a^{2} + 9) (2 a^{2} + 5)$
$= (2 a^{2})^{2} + (9 + 5) 2 a^{2} + (9) \times (5)$
$= 4 a^{2} + (14) 2 a^{2} + 45$
$= 4 a^{4} + 28 a^{2} + 45$ .

Therefore, option $B$ is correct.

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