One of the factors of the expression $(2 a + 5 b)^{3} + (2 a - 5 b)^{3}$ would be

4 a

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10 b

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2 a + 5 b

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2 a - 5 b

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Solution

The correct option is A $4 a$
$(2 a + 5 b)^{2} + (2 a - 5 b)^{3}$
$(2 a)^{3} + (5 b)^{3} + 3 (2 a)^{2} 5 b + 3 (2 a) (5 b)^{2} + (2 a)^{3} - (5 b)^{3}$
$- 3 (2 a)^{2} 5 b + 3 (2 a) (5 b)^{2}$
$= 16 a^{3} + 300 a b^{2}$
$= 4 a [4 a^{2} + 75 b^{2}]$
$\Rightarrow 4 a$ is a factor

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