Multiplying by a Monomial

Multiplying by a Monomial

Monomials can be multiplied times other monomials, times binomials, times trinomials, and times polynomials in general.

Multiplying by a monomial may involve:

1. applying rules for dealing with exponents
2. using the distributive property
3. remembering rules for multiplying signed numbers

Multiply a Monomial by a Monomial:
When multiplying monomials, use the product rule for exponents.
x^m • xⁿ = x^m+n

Multiply a Monomial by a Polynomial:
When multiplying a monomial by a polynomial, use the distributive property.
The traditional statement of the distributive property shows a monomial times a binomial:
a • (b + c) = a • b + a • c
This statement can be expanded when more terms are involved:
a • (b + c + d + … + n) = ab + ac + ad + … + an.

Monomial Multiplication with Algebra Tiles:
This set up of Algebra tiles gives you a “visual” demonstration of multiplying monomial x times binomial (x + 3).