MULTIPLICATION OF MONOMIALS AND BINOMIALS 5-9
Multiplying a monomial by a polynomial is just the Distributive Property
You'll need to remember your power rules because you'll be MULTIPLYING SAME BASES
and then combining only LIKE TERMS.
EXAMPLE:
3x³ ( 2x² - 3x + 10)
3x³(2x²) + 3x³(- 3x) + 3x³(10)
6x⁵ - 9 x⁵ + 30x³
(no like terms to combine in this one!)
When you multiply a binomial by another binomial, I used to think of it as DOUBLE Distributive Property...See if you can figure out why!

Multiplying a binomial by another binomial:
FOILing binomials:
This is a memory device so you won't forget to multiply any of the factors!
First - first term in each binomial (terms on the left)
Outside - two outside terms in each binomial ( the first one in the
left parentheses and the second one in the right parentheses)
Inside - two inside terms (the terms right next to each other in the
different parentheses - the second one in the first parentheses
and the first one in the second parentheses)
Last - second term in each binomial (terms on the right)

I know this may seem overwhelming when you first see it,
but after you practice it, it does make sense.
It helps a lot of students to not forget any of the 4 multiplications!
EXAMPLE: (5x + 6)(3x - 7)
F O I L
FIRST OUTSIDE INSIDE LAST
= (5x)(3x) + (5x)(-7) + (6)(3x) + (6)(-7)
Simplify: 15x² + (-35x) + 18x - 42
Combine like terms: 15x² + -17x - 42
By the way, you can also do this in different orders --- as long as you multiply each term in one parentheses by each term in the other parentheses.
There are other ways to do the same problem:

Showed you the "box" method that allows you to use any order and protects you from ever missing one of the four multiplications. ( I can't get a table embedded here so make sure to look at your notes about the box method-- or email me.
5x +6
3x 15x² 18x
-7 -35x -42



15x²+ 18 x – 35x -42 =
15x² – 17x – 42
Also showed you "unibrow" method where you use arrows to show which terms you are multiplying. THIS IS HOW I LEARNED AND SEE IF YOU CAN FIGURE OUT WHY I USED TO THINK OF IT AS DOUBLE DISTRIBUTIVE PROPERTY!
I can't really show this on this website so watch carefully in class!