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

3 a^{2} - 2 b^{2} + 4 c^{2} - a b + 6 b c + 7 a c

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- 3 a^{2} + 2 b^{2} + 4 c^{2} - a b + 6 b c - 7 a c

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a c + 4 b c + 4 c^{2} - 3 a^{2} - a b + 2 c

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a c + 4 b c + 4 c^{2} + 3 a^{2} - a b + 2 c

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Solution

The correct option is D $- 3 a^{2} + 2 b^{2} + 4 c^{2} - a b + 6 b c - 7 a c$
$3 a (a + b + c) - 2 b (a + b + c)$

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

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

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

Required difference $\Rightarrow 4 c (- a + b + c) - (3 a^{2} - 2 b^{2} + a b + 3 a c - 2 b c)$

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

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

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State True or False:

On subtracting $a^{2} + a b + b^{2}$ from $4 a^{2} - 3 a b + 2 b^{2}$ , the answer is $3 a^{2} - 4 a b + b^{2}$ .

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a b c^{2} x^{2} + (3 a^{2} + b^{2}) c x - 6 a^{2} - a b + 2 b^{2} = 0

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