Question

What is the standard form of `y= (-7x-x^2)(x+3) -(x-12)^3`?

Answer 1

`y=-2x^3+26x^2-453x+1728`
happens to be the standard form
`y=ax^3+bx^2+cx+d`

Explanation:

Given:
`y=(-7x-x^2)(x+3)-(x-12)^3`
Expanding rhs and simplifying
`y=-7x^2-x^3-21x-3x^2-(x^3-3xx12x^2+3xx12^2x-12^3)`
`y=-7x^2-x^3-21x-3x^2-x^3+3xx12x^2-3xx144x+1728)`
`y=(-1-1)x^3+(-7-3+36)x^2+(-21-432)x+1728`
`y=-2x^3+26x^2-453x+1728`