a^3 1a^3 =(a 1a)(a^2+1a^2+a×1a) #160; ........ #160; Using a^3 b^3=(a b)(a^2+ab+b^2) =(a 1a)(a^2+1a^2+1) ...

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Algebraic Identities

Factorize a...

Question

Factorize $a^{3} - \frac{1}{a^{3}}$ .

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Solution

$a^{3} - \frac{1}{a^{3}}$

$= (a - \frac{1}{a}) (a^{2} + \frac{1}{a^{2}} + a \times \frac{1}{a})$ ........ Using $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$

$= (a - \frac{1}{a}) (a^{2} + \frac{1}{a^{2}} + 1)$

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