Factorise by grouping method:

$a^{2} + 4 b^{2} - 3 a + 6 b - 4 a b$

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Solution

$a^{2} + 4 b^{2} - 3 a + 6 b - 4 a b$

= a² + 4b² - 4ab - 3a + 6b

= a² + (2b)² - 2 × a × (2b) - 3(a - 2b)

=(a - 2b)²- 3(a - 2b)

=(a - 2b)[(a - 2b)- 3]

=(a - 2b)(a - 2b - 3)

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