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

Again we’ll use the distributive property: and the answer is 
Ex. 3 ( Binomial times a binomial)
Multiply:
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 inside terms gives us 
Ex. 4 (Binomial times a trinomial )
Multiply:
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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