Some people use the letters FOIL as a strategy
for making sure they have multiplied all the terms.
Use the FOIL approach to multiply
3x plus 2 times 5x minus 7.
I'm actually not one of those people
who likes to use the FOIL letters,
because it's just a form of memorization
as opposed to realizing that you're just
using the distributive property twice.
But with that said, let's actually
use FOIL so you see that it actually
is the same thing as using the distributive property twice.
So just to remember FOIL, it literally stands
for-- so F-O-I-L. The F in FOIL stands for First.
The O stands for Outside.
The I stands for Inside.
And the L stands for Last.
So not only do you have to remember FOIL,
you have to remember what each of these letters
actually stand for.
But let's see how that applies to multiplying these two
binomials.
So we have 3x plus 2 times 5x minus 7.
So we're starting with the first,
we're starting with the F.
We have to multiply the first terms in each of the binomials.
So that's going to be 3x times 5x.
Then we do the outside terms.
So that's going to be the 3x times the negative 7.
So this is going to be plus 3x times negative 7.
Then we want to do the inside terms.
Then we want to do-- I'll do that in green-- then
we want to do the inside terms.
So that's the 2 and the 5x.
So that's plus 2 times 5x.
And then we want to do the last terms.
And the last terms are the 2 and the negative 7,
so plus 2 times negative 7.
And we end up getting 3x times 5x is 15x squared, plus--
or I should say minus because there's
going to be a negative sign here.
So 3x times negative 7 is negative 21x.
And then we have 2 times 5x is-- let
me do that in that same shade of green.
So this is plus 10x.
And then 2 times negative 7 is negative 14,
or now it's minus 14.
And we can add these two middle terms together.
If we have negative 21x and then we add 10x to that,
that gives us negative 11x.
So this right here is negative 11x.
And then these other terms over here.
We have 15x squared minus 11x minus 14.
So we just used FOIL.
What I want to do is show you this
is the same thing as applying the distributive property
twice.
So if we have-- I'll rewrite the problem-- 3x
plus 2 times 5x minus 7.
What we could do is distribute the 5x minus 7.
We can multiply that times the 3x.
And we could also multiply that--
and let me make it clear when I say
that, I mean this whole 5x minus 7-- we can multiply it times
the 3x and by the 2.
We're just distributing it over the 3x plus 2.
So we get literally 3x times 5x minus 7
plus 2 times 5x minus 7.
And then this gives us 3x times 5x is going to be 15x squared.
3x times negative 7 is going to be negative 21x.
And remember, in this step we're just
applying the distributive property again.
So then we have 2 times 5x is going to be 10x, so plus 10x.
And then we have 2 times negative 7 is negative 14.
So we actually got the exact same result
that we did when we applied FOIL.
And when you simplify it you get this answer again.