Question

What is the standard form of `y= (x+3)(x-9) (6-x)`?

Answer 1

`y=~x^3+12x^2-9x-162`

Explanation:

All we do is simplify the equation.

In order to simplify the binomials, we use the FOIL method.

Keep in mind that this only works for only two of the binomials. After this, we have a trinomial and a binomial.

Let's start with the first 2 binomials.

`y=(x+3)(x-9)(6-x)`

`=(x^2+3x-9x-27)(6-x)`

Now we add like terms in the first bracket.

`=(x^2-6x-27)(6-x)`

Now for this situation, we multiply each term in the trinomial with each term in the binomial.

`=(color(red)(x^2)color(blue)(-6x)color(purple)(-27))(6-x)`

`=color(red)(6x^2-x^3)color(blue)(-36x+6x^2)color(purple)(-162+27x)`

Now we add like terms.

`=~x^3+12x^2-9x-162`

And that's it.

Hope this helps :)