(2x+5x) (4x2-10+25x2) =

8 x^{3} + \frac{125}{x^{3}}

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4 x^{3} + \frac{125}{x^{2}}

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4 x^{2} + \frac{25}{x^{3}}

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8 x^{2} + \frac{25}{x^{2}}

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Solution

The correct option is A $8 x^{3} + \frac{125}{x^{3}}$
The given expression is

$(2 x + \frac{5}{x}) (4 x^{2} - 10 + \frac{25}{x^{2}})$
$T a k i n g a = 2 x a n d b = \frac{5}{x}$ , we get
$(a + b) (a^{2} - a b + b^{2})$
Using identity we have

$(a + b) (a^{2} - a b + b^{2})$ = $a^{3} + b^{3}$
Hence,
$(2 x + \frac{5}{x}) (4 x^{2} - 10 + \frac{25}{x^{2}})$ = $(2 x)^{3} + (\frac{5}{x})^{3}$
= $8 x^{3} + \frac{125}{x^{3}}$

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