Question

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

Answer 1

`y = 3x^3 + 81x^2 + 486x`

Explanation:

The general standard form of a cubic function is

`y = ax^3 + bx^2 + cx + d`

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

[Solution]
`y = 3x (x + 9) (x + 18)`
`y = 3x(x^2 + 18x + 9x + 162)`
`y = 3x (x^2 + 27x + 162)`
`y = 3x^3 + 81x^2 + 486x`

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 = 3x(x+9)(x+18)`
`y = (3x^2 + 27x)(x+18)`
`y = 3x^3 + 54x^2 + 27x^2 + 486`
`y = 3x^3 + 81x^2 + 486`