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Solving a Quadratic Equation by Completion of Squares Method

Add :- 4a2b...

Question

Add :- $4 a^{2} b - 2 b^{2} + 3 c^{2} a + 4 a b c 5$ and $a^{2} b + b^{2} - 2 c^{2} + 8 a b$

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Solution

To add :- $4 a^{2} b - 2 b^{2} + 3 c^{2} a + 4 a b c$
and $a^{2} b + b^{2} - 2 c^{2} + 8 a b$
$\Rightarrow (4 a^{2} b + a^{2} b) + (- 2 b^{2} + b^{2}) + (3 c^{2} a + 4 a b c - 2 c^{2} + 8 a b)$
$\Rightarrow 5 a^{2} b - b^{2} + c^{2} (3 a - 2) + 4 a b (c + 2)$

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