How do you factor completely 3x^3y - 27x^2y + 54xy?

Apr 9, 2016

$3 x y \left(x - 3\right) \left(x - 6\right)$

Explanation:

Take $3 x y$ out as a common factor:
$3 x y \left({x}^{2} - 9 x + 18\right)$

Hence, factorise the subsequent quadratic:
$3 x y \left({x}^{2} - 9 x + 18\right)$
$= 3 x y \left(x - 3\right) \left(x - 6\right)$