A monomial is an algebraic expression consisting of a single term of the formwhere a is a real number and n is a non-negative integer.

A polynomial is an algebraic expression consisting of monomials as terms or addends.

A monomial contains one term, a binomial contains 2 terms, and a trinomial contains 3 terms.

The degree of a monomial is the sum of the exponents on the variables.

The degree of a polynomial is the degree of the term of the highest degree.

ADDITION AND SUBTRACTION OF POLYNOMIALS

To add polynomials, add the coefficients of like terms.

Example

To subtract polynomials, .subtract the coefficients of like terms.

Example

Multiplying a polynomial by a monomial:

EXAMPLE

Multiplying Binomials

EXAMPLE

Multiplying a Trinomial by a Binomial

EXAMPLE

The FOIL Method is used to multiply two binomials. The idea is to multiply the first terms of each binomial, followed by the outer terms of each binomial, then the inner terms of each binomial, and finally the last terms of each binomial.

EXAMPLE

NOTE: The first terms are x and x. The outer terms are x and -3. The inner terms are 4 and x. The last terms are 4 and -3.

EXAMPLE

SPECIAL PRODUCTS

The square of a binomial:

The square of a binomial is the sum of the square of the first term, twice the product of the first and last term, and the square of the last term.

A Sum times a Difference

A sum times a difference is the difference of the square of the first term and the square of the second term.