We know a^3 b^3 =(a b) (a^2 +ab +b^2) a^3 27/a^3= a^3 (3/a)^3 = (a 3/a) (a^2 +3 +(3/a)^2) = (a 3/a) (a^2 +3+9/a^2) ...

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Factorisation Using Algebraic Identities

Factorise: a3...

Question

Factorise:

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

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Solution

$W e k n o w a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2}) a^{3} - \frac{27}{a^{3}} = a^{3} - (\frac{3}{a})^{3} = (a - \frac{3}{a}) (a^{2} + 3 + (\frac{3}{a})^{2}) = (a - \frac{3}{a}) (a^{2} + 3 + \frac{9}{a^{2}})$

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