Subtract $5 a^{2} - 7 a b + 5 b^{2}$ from $3 a b - 2 a^{2} - 2 b^{2}$ [2 marks]

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Solution

$3 a b - 2 a^{2} - 2 b^{2} - (5 a^{2} - 7 a b + 5 b^{2}) = 3 a b - 2 a^{2} - 2 b^{2} - 5 a^{2} + 7 a b - 5 b^{2}$
$= 3 a b + 7 a b - 2 a^{2} - 5 a^{2} - 2 b^{2} - 5 b^{2}$
$= 10 a b - 7 a^{2} - 7 b^{2}$
$= - 7 a^{2} - 7 b^{2} + 10 a b$ (2 marks)

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