Answer:
[tex]y=3x^2+9x-30[/tex]
Step-by-step explanation:
To multiply [tex](3x+15)[/tex] with [tex](x-2)[/tex] we can use a method called the FOIL method. FOIL is an acronym standing for First, Outer, Inner, Last. This is the order in which we need to multiply. The first terms of each multiplier are [tex]3x[/tex] and [tex]x[/tex]. Therefore, we multiply these two terms to get [tex]3x^2[/tex]. The outer terms are [tex]3x[/tex] and [tex]-2[/tex]. Once again, we multiply these terms.
[tex](3x)(-2)=-6x[/tex]
Now, our equation looks like this: [tex]y=3x^2-6x[/tex]. We're not finished yet though. Next, we need to multiply the inner terms, [tex]15[/tex] and [tex]x[/tex]. This comes out as simply [tex]15x[/tex]. Now our equation looks like this: [tex]y=3x^2-6x+15x[/tex]. We just need to multiply the last terms, [tex]15[/tex] and [tex]-2[/tex]. This comes out as [tex]-30[/tex].
Our equation at this point has been fully multiplied:
[tex]y=3x^2-6x+15x-30[/tex]
We can see that we still have two like terms, [tex]-6x[/tex] and [tex]15x[/tex]. These can be combined to simply [tex]9x[/tex]. Our final equation, then, is this: [tex]y=3x^2+9x-30[/tex]
