Subtract $3 a (a + b + c) - 2 b (a - b + c)$ from $4 c (- a + b + c)$ .

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Solution

We have to subtract $3 a (a + b + c) - 2 b (a - b + c)$ from $4 c (- a + b + c)$ .
$\begin{array}{rcl} 4 c (- a + b + c) - \{3 a (a + b + c) - 2 b (a - b + c)\} \\ = & (- 4 ac + 4 bc + 4 c^{2}) - \{(3 a^{2} + 3 ab + 3 ac) - (2 ab - 2 b^{2} + 2 bc)\} \\ = & - 4 ac + 4 bc + 4 c^{2} - (3 a^{2} + 3 ab + 3 ac - 2 ab + 2 b^{2} - 2 bc) \\ = & - 4 ac + 4 bc + 4 c^{2} - (3 a^{2} + 2 b^{2} + 1 ab - 2 bc + 3 ac) \\ = & - 4 ac + 4 bc + 4 c^{2} - 3 a^{2} - 2 b^{2} - 1 ab + 2 bc - 3 ac \\ = & - 3 a^{2} - 2 b^{2} + 4 c^{2} - ab + 6 bc - 7 ac \end{array}$
Therefore the required answer is $- 3 a^{2} - 2 b^{2} + 4 c^{2} - ab + 6 bc - 7 ac$ .

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