subtract: $3 a (a + b + c) - 2 b (a - b + c)$ from $4 c (- a + b + c)$

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Solution

$4 c (- a + b + c) - [3 a (a + b + c) - 2 b (a - b + c)]$
$= - 4 a c + 4 b c + 4 c^{2} - [3 a^{2} + 3 a b + 3 a c - 2 a b + 2 b^{2} - 2 b c]$
$= - 4 a c + 4 b c + 4 c^{2} - 3 a^{2} - 3 a b - 3 a c + 2 a b - 2 b^{2} + 2 b c$
$= - 3 a^{2} - 2 b^{2} + 4 c^{2} - a b + 6 b c - 7 a c$

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