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

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

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

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

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

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Solution

The correct option is A $(a + b - c) (a - b + c)$
Given $a^{2} - (b - c)^{2}$
This is of the form $a^{2} - b^{2} = (a + b) (a - b)$ . Therefore,
$a^{2} - (b - c)^{2} = (a + b - c) [a - (b - c)]$
$= (a + b - c) (a - b + c)$

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