Factorise :

$a^{2} - b^{2} - c^{2} + 2 b c$

(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 B $(a + b - c) (a - b + c)$
$a^{2} - b^{2} - c^{2} + 2 b c$
$= a^{2} - (b^{2} + c^{2} - 2 b c)$
$= a^{2} - (b - c)^{2}$
$= (a + b - c) (a - b + c)$

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Similar questions

(a^{2} - 2 b c - b^{2} - c^{2}) \div (a - b - c) (a + b + c)

a^{2} + b^{2} + c^{2} - a b - b c - c a = \frac{1}{2} [{(b - c)}^{2} + {(c - a)}^{2} + {(a - b)}^{2}]

a² + b² + c² - ab - bc - ca equals:

a + b + c = 0

\frac{(b + c)^{2}}{b c} + \frac{(c + a)^{2}}{c a} + \frac{(a + b)^{2}}{a b}

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