# What is the standard form of  y=3x(x+9)(x+18) ?

Jan 28, 2016

$y = 3 {x}^{3} + 81 {x}^{2} + 486 x$

#### Explanation:

The general standard form of a cubic function is

$y = a {x}^{3} + b {x}^{2} + c x + d$

Since what you are currently given is the factored form, you need to expand the equation to get the standard form.

[Solution]
$y = 3 x \left(x + 9\right) \left(x + 18\right)$
$y = 3 x \left({x}^{2} + 18 x + 9 x + 162\right)$
$y = 3 x \left({x}^{2} + 27 x + 162\right)$
$y = 3 {x}^{3} + 81 {x}^{2} + 486 x$

For this example, I chose to expand the 2nd and 3rd terms first before inputting in the 1st. Note that you may choose whichever terms you want to expand first but I suggest that you consider expanding those that would not give you really big numbers so as to lessen the probability that you will incur errors in calculations.

[Solution if choose to expand the 1st and 2nd term first]
$y = 3 x \left(x + 9\right) \left(x + 18\right)$
$y = \left(3 {x}^{2} + 27 x\right) \left(x + 18\right)$
$y = 3 {x}^{3} + 54 {x}^{2} + 27 {x}^{2} + 486$
$y = 3 {x}^{3} + 81 {x}^{2} + 486$