Simplify
$(a + b) (2 a - 3 b + c) - (2 a - 3 b) c$ .

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Solution

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

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