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

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Answer 1 · 2017-10-29T01:12:54

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

All we do is simplify the equation.

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

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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 :)