Monomials


Monomials and the GCF
A monomial is a number, a variable raised to a whole number, or a product of a number and one or more variables.
 
Examples: 12x2y,   3mn,   64w3y2
 

In algebra, a polynomial is the sum of two or more monomials.
 
Examples:   (12x2y2 + 3x3y2);   (12m + 64);   and   (3p − 64p3q + 12pq2)

A polynomial with 2 terms is known as a binomial, and it's the sum of two monomials.  A polynomial with 3 terms is known as a trinomial, and so on.
 
 
 
 
 
Factoring Monomials

To factor a monomial means to write the monomial as a product of its factors.

Finding the greatest common factor (GCF)


 
 
 
Power of a Power Property

To raise a monomial to a power, multiply exponents for each variable by the external power; and raise each numeric factor to the external power.

Example:

Simplify:  (2t 4p3)4
 
 
 
 


Practice

Simplify the following monomials.
 









 
 






Find the GCF for the following.






















Answers
 
1.)  27x7
2.)  x6
3.)  81x12
4.)  4mn3
5.)  8x3y2