Question
Subtract: $3a(a + b + c) - 2b(a - b + c)$ from $4c(-a + b + c)$.
✓
Answer
$ 4 c(-a+b+c)-[3 a(a+b+c)-2 b(a-b+c)] $
$ =-4 a c+4 b c+4 c^2-\left[3 a^2+3 a b+3 a c-2 a b+2 b^2-2 b c\right] $
$ =-4 a c+4 b c+4 c^2-\left[3 a^2+2 b^2+3 a b-2 b c+3 a c-2 a b\right] $
$ =-4 a c+4 b c+4 c^2-\left[3 a^2+2 b^2+a b+3 a c-2 b c\right] $
$ =-4 a c+4 b c+4 c^2-3 a^2-2 b^2-a b-3 a c+2 b c $
$ =-3 a^2-2 b^2+4 c^2-a b+4 b c+2 b c-4 a c-3 a c $
$ =-3 a^2-2 b^2+4 c^2-a b+6 b c-7 a c $
$ =-4 a c+4 b c+4 c^2-\left[3 a^2+3 a b+3 a c-2 a b+2 b^2-2 b c\right] $
$ =-4 a c+4 b c+4 c^2-\left[3 a^2+2 b^2+3 a b-2 b c+3 a c-2 a b\right] $
$ =-4 a c+4 b c+4 c^2-\left[3 a^2+2 b^2+a b+3 a c-2 b c\right] $
$ =-4 a c+4 b c+4 c^2-3 a^2-2 b^2-a b-3 a c+2 b c $
$ =-3 a^2-2 b^2+4 c^2-a b+4 b c+2 b c-4 a c-3 a c $
$ =-3 a^2-2 b^2+4 c^2-a b+6 b c-7 a c $
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