Unit 4: Algebraic Expressions

  1. Monomials

– A monomial is the product of a number (coefficient) and one or more letters (variable)

-The degree of a monomial is the sum of the factors in its variable.

-Only like monomials can be added together. If monomials are not like, the addition sign must be left in the expression.

-Two monomials are like when they have the same literal part.


To multiply monomials you multiply the coefficients and the variables, following the rules for dealing with powers. The result is always a monomial.

  1. Polynomials

-A polynomial is the sum of two or more monomials. The monomials that comprise it are called terms. The degree of a polynomial is the term with the highest degree.

-To add two polynomials from the other, you add the opposite of the polynomial being subtracted.

BEAR IN MIND! – You obtain the additive inverse, or opposite of a polynomial by changing the sign of every term.

DON`T FORGET – If a set of brackets has a minus sign in front of it you need to change all of the signs inside the brackets.

Polynomial Products:

– To multiply a monomial by a polynomial, you multiply the monomial by each of the polynomial’s terms.

– To multiply two polynomials, you multiply each term in one polynomial by each term in the other, and then add the like monomials.

  1. Special Binomial Products