Factorise:
$9 a^{2} + 3 a - 8 b - 64 b^{2}$

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Solution

$9 a^{2} + 3 a - 8 b - 64 b^{2} = 9 a^{2} - 64 b^{2} + 3 a - 8 b = (3 a)^{2} - (8 b)^{2} + 3 a - 8 b = (3 a - 8 b) (3 a + 8 b) + 1 (3 a - 8 b) = (3 a - 8 b) (3 a + 8 b + 1)$

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9 a^{2} + 3 a - 8 b - 64 b^{2}

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49 a^{2} - 64 b^{2}

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(3 a - \frac{1}{2}) (3 a - \frac{1}{2})

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