1 27a^3 = (1)^3 (3a)^3 =(1 3a) [ 1^2 + 1 × 3a+ (3a)^2] = (1 3a) (1+3a + 9a^2) ...

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Algebraic Identities

Factorize: 1-...

Question

Factorize:

$1 - 27 a^{3}$

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Solution

$1 - 27 a^{3} = (1)^{3} - (3 a)^{3} = (1 - 3 a) [1^{2} + 1 \times 3 a + (3 a)^{2}] = (1 - 3 a) (1 + 3 a + 9 a^{2})$

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27 a^{3} + \frac{1}{64 b^{3}} + \frac{27 a^{2}}{4 b} + \frac{9 a}{16 b^{2}}

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$8 x^{3} y^{3} + 27 a^{3}$

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