Simplify: $(- a - b + c)^{2} - (a + b - c)^{2}$

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Solution

$(- a - b + c)^{2} - (a + b - c)^{2}$
Using $a^{2} - b^{2} = (a + b) (a - b)$
$= [(- a - b + c) + (a + b - c)] [(- a - b + c) - (a + b - c)]$
$= (- a - b + c + a + b - c) (- a - b + c - a - b + c)$
$= 0 (- a - b + c - a - b + c)$
$= 0$

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