# What is the standard form of y=2x(3-x)(6-x)?

Jan 31, 2016

$y = 2 x \left(3 - x\right) \left(6 - x\right)$

First solve $\left(3 - x\right) \left(6 - x\right)$ using foil method:

Foil method:

So,
$\left(3 - x\right) \left(6 - x\right) = 18 - 3 x - 6 + {x}^{2} = \left(18 - 9 x + {x}^{2}\right) = \left({x}^{2} - 9 x + 18\right)$ In standard notation.

$\rightarrow y = 2 x \left({x}^{2} - 9 x + 18\right)$

Use distributive property to multiply:

$\rightarrow y = 2 {x}^{3} - 18 {x}^{2} + 36 x$