Simplify:
$a^{2} - 3 b^{2} - c^{2} - 2 a b + 4 b c$ .

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Solution

Now,
$a^{2} - 3 b^{2} - c^{2} - 2 a b + 4 b c$
$= (a^{2} - 2 a b + b^{2}) - 4 b^{2} - c^{2} + 4 b c$
$= (a - b)^{2} - (2 b - c)^{2}$
$= (a + b - c) (a - b + c)$ .

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