Simplify:
$(a + b + c) \times (a + b - c)$

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

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

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

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

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Solution

The correct option is B
$a^{2} + b^{2} - c^{2} + 2 a b$

$(a + b + c) \times (a + b - c)$

$= [(a + b) + c] \times [(a + b) - c]$ $= (a + b)^{2} - c^{2}$
[Using identity $(a + b) (a - b) = a^{2} - b^{2}$ ]

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

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