The correct option is D ( a 3/a ) ( a^2+3+9/a^2 ) a^3 27a^3 Using, a^3 b^3=(a b)(a^2+ab+b^2) a^3 (3a)^3 =(a 3a)(a^2+(a)(3a)+(3a)^2 ...

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Algebraic Identities

Factorize : ...

Question

Factorize :
$a^{3} - \frac{27}{a^{3}}$

(a - \frac{3}{a}) (a^{2} + 1 + \frac{9}{a^{3}})

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(a - \frac{5}{a}) (a^{2} + 3 + \frac{9}{a^{2}})

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(2 a - \frac{2}{a}) (a^{2} + 1 + \frac{9}{a^{3}})

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(a - \frac{3}{a}) (a^{2} + 3 + \frac{9}{a^{2}})

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Solution

The correct option is D $(a - \frac{3}{a}) (a^{2} + 3 + \frac{9}{a^{2}})$
$a^{3} - \frac{27}{a^{3}}$
Using,
$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
$a^{3} - (\frac{3}{a})^{3}$
$= (a - \frac{3}{a}) (a^{2} + (a) (\frac{3}{a}) + (\frac{3}{a})^{2}$
$= (a - \frac{3}{a}) (a^{2} + 3 + \frac{9}{a^{2}})$

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