Find the sum of:
(ix) $4 a^{2} + 5 b^{2} - 6 a b, 3 a b, 6 a^{2} - 2 b^{2}$ and $4 b^{2} - 5 a b$

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Solution

Step: Find the sum of given expressions
We need to add $(4 a^{2} + 5 b^{2} - 6 a b), (3 a b), (6 a^{2} - 2 b^{2})$ and $(4 b^{2} - 5 a b)$
$= (4 a^{2} + 5 b^{2} - 6 a b) + (3 a b) + (6 a^{2} - 2 b^{2}) + (4 b^{2} - 5 a b)$
$= (4 a^{2} + 6 a^{2}) + (5 b^{2} - 2 b^{2} + 4 b^{2}) + (- 6 a b + 3 a b - 5 a b)$ [Grouping like terms]
$= 10 a^{2} + (3 b^{2} + 4 b^{2}) + (- 3 a b - 5 a b)$
$= 10 a^{2} + 7 b^{2} - 8 a b$
Hence, the answer is $10 a^{2} + 7 b^{2} - 8 a b .$

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