Which of the following are the factors of
$27 a^{2} - 12 b^{2} ?$

3

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(3 b - 2 a)

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(3 a - 2 b)

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(3 a + 2 b)

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Solution

The correct options are
A $3$
C $(3 a - 2 b)$
D $(3 a + 2 b)$
Given, the expression is
$27 a^{2} - 12 b^{2} .$
The above expression can be written as,
$27 a^{2} - 12 b^{2}$
$= 3 (9 a^{2} - 4 b^{2})$
$= 3 [(3 a)^{2} - (2 b)^{2}]$
$[Using the identity: a^{2} - b^{2} = (a + b) (a - b)]$
$= 3 (3 a + 2 b) (3 a - 2 b)$
Therefore,
3, (3a + 2b) and (3a - 2b) are the three factors of the given expression.

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