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

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

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

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

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

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Solution

The correct option is A $(b + c + a) (b + c - a)$
$b^{2} + c^{2} + 2 b c - a^{2}$
$= (b + c)^{2} - a^{2}$
$= (b + c + a) (b + c - a)$

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

a^{3} + b^{3} + c^{3} - 3 a b c

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\frac{a^{2} + a b + b^{2}}{b^{2} + b c + c^{2}} = \frac{a}{c}

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

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

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