Factorise: $1 - 27 a^{3}$

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

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(1 - a) (1 - 3 a + a^{2})

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(1 - 3 a) (1 + 3 a + a^{2})

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

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Solution

The correct option is D $(1 - 3 a) (1 + 3 a + 9 a^{2})$
Given expression is $1 - 27 a^{3}$
We can write the above expression as:
$= 1^{3} - (3 a)^{3}$
Using the formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ , we get:
$\Rightarrow (1 - 3 a) [1^{2} + 1 \times 3 a + (3 a)^{2}]$
$∴ (1 - 3 a) (1 + 3 a + 9 a^{2})$

Hence, option D is correct.

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Similar questions

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Evaluate : $(3 a - \frac{1}{2}) (3 a - \frac{1}{2})$

(3 a - \frac{1}{2}) (3 a - \frac{1}{2})

Factorise:

$9 a^{2} + \frac{1}{9 a^{2}} - 2 - 12 a + \frac{4}{3 a}$

Find the value of : $(3 a - \frac{1}{2}) (3 a - \frac{1}{2})$

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