Multiplying Polynomials

What does mean?

So what is ? Well, it would be or . Now look back at the
exponents. When you add 5 and 2 the result is 7, right? This is the first rule of exponents:
*When multiplying like bases , add exponents. (ex. )

Ex. 1

Simplify :

*Since the bases are the same, I can add the exponents and get
*Again, the bases are the same so add the exponents and get . A
common mistake here is to multiply the 2s and get . This is incorrect,
only add the exponents, don't multiply the bases.
*Don't let this one throw you just because it has more factors .
Multiply the coefficients as you normally would and only add the
exponents on the like bases . So the answer is

Ex. 2 (Monomial times a polynomial )


We’ll use the distributive property :
Now it’s just a matter of multiplying monomials and the
Again we’ll use the distributive property:
and the answer is

Ex. 3 ( Binomial times a binomial)


There are two methods that we can use here. First, we can
use the distributive property by breaking that first binomial
into two monomials: That will
give us or
. Notice that the two inside terms are
like so
we combine those and get The other
method used to multiply binomials is the FOIL method.
This is an acronym that stands for First Outside Inside Last.
This is the order in which you multiply. First represents the
first term in each binomial: x(x). Outside represents the
terms on the outside of each binomial: x(2). Inside
represents the terms on the inside of the binomials: 3(x).
And Last represents the last term in each binomial: 3(2).
When we multiply using the FOIL method we get
which also gives us
Whether you use the distributive property or the FOIL
method, you should get:
That gives us
And again, combining the
terms gives us

Ex. 4 (Binomial times a trinomial )


Here again we have to use the distributive property:

When we multiply, we get
And combining
like terms gives us our answer:
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