( 3x 5 x #160; ) #160; ^ 3 ⇒ Using ( a b ) #160; ^ 3 =a^3 3ab( a b ) #160; b^3 ⇒ Here, a=3x, #160; b= 5 x so, ...

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Algebraic Identities

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Question

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${(3 x - \frac{5}{x})}^{3}$

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Solution

${(3 x - \frac{5}{x})}^{3}$
$\Rightarrow$ Using ${(a - b)}^{3} = a^{3} - 3 a b (a - b) - b^{3}$
$\Rightarrow$ Here, $a = 3 x,$ $b = \frac{5}{x}$
so, ${(3 x)}^{3} - 3 (3 x) (\frac{5}{x}) (3 x - \frac{5}{x}) - {(\frac{5}{x})}^{3}$
$27 x^{3} - 45 (3 x - \frac{5}{x}) - \frac{125}{x^{3}}$
$27 x^{3} - 135 x + \frac{225}{x} - \frac{125}{x^{3}} .$
Hence, the answer is $27 x^{3} - 135 x + \frac{225}{x} - \frac{125}{x^{3}} .$

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