Question
Factorise the following:$2a^3 + 5a^2b - 12ab^2$
✓
Answer
$2a^3 + 5a^2b - 12ab^2$
$= 2a^3 + 8a^2b - 3a^2b - 12ab^2$
$= 2a^2(a + 4b) - 3ab(a + 4b)$
$= (a + 4b)(2a^2 - 3ab)$
$= (a + 4b)a(2a - 3b)$
$= a(a + 4b)(2a - 3b).$
$= 2a^3 + 8a^2b - 3a^2b - 12ab^2$
$= 2a^2(a + 4b) - 3ab(a + 4b)$
$= (a + 4b)(2a^2 - 3ab)$
$= (a + 4b)a(2a - 3b)$
$= a(a + 4b)(2a - 3b).$
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