Factorize:
$a^{2} - 81 (b - c)^{2}$ .

(a - 9 b - 9 c) (a - 9 b + 9 c)

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(a + 9 b + 9 c) (a - 9 b + 9 c)

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(a + 9 b - 9 c) (a - 9 b + 9 c)

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(a + 9 b - 9 c) (a - 9 b - 9 c)

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Solution

The correct option is A $(a + 9 b - 9 c) (a - 9 b + 9 c)$
$a^{2} - 81 (b - c)^{2}$
$= a^{2} - (9 b - 9 c)^{2}$
Using [ $a^{2} - b^{2} = (a + b) (a - b)$ ], we get
$= (a + 9 b - 9 c) (a - 9 b + 9 c)$

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