Factorise $a^{2} - 81 (b - c)^{2}$

(a+ 81b- 81c)(a-81b-81c)

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

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

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

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Solution

The correct option is B
(a+ 9b- 9c)(a-9b-9c)

Given expression is $a^{2} - 81 (b - c)^{2}$
= $a^{2} - (9 (b - c))^{2}$
We know $(a^{2} - b^{2})$ = $(a + b) (a - b)$
= $(a - 9 (b - c)) (a + 9 (b - c))$
= $(a - 9 b + 9 c) (a + 9 b - 9 c)$

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