Question
Factorise the following:$2x^3 + 5x^2y - 12xy^2$
✓
Answer
$2x^3 + 5x^2y - 12xy^2$
$= 2x^3 + 8x^2y - 3x^2y - 12xy^2$
$= 2x^2(x + 4y) - 3xy(x + 4y)$
$= (x + 4y)(2x^2 - 3xy)$
$= (x + 4y)x(2x - 3y)$
$= x(x + 4y)(2x - 3y).$
$= 2x^3 + 8x^2y - 3x^2y - 12xy^2$
$= 2x^2(x + 4y) - 3xy(x + 4y)$
$= (x + 4y)(2x^2 - 3xy)$
$= (x + 4y)x(2x - 3y)$
$= x(x + 4y)(2x - 3y).$
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