Multiplying by a Monomial
 Topic Index | Algebra Index | Regents Exam Prep Center

 

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

 

Tools for Dealing
with Monomials
Distributive Property
a(b + c) = ab + ac

Rules for Exponents

Multiplying Signed Numbers
(+) • (+) = (+)
(+) • (-) = (-)
(-) • (+) = (-)
(-) • (-) = (+)

 

Example 1:
monomial • monomial

   (4x3) • (3x2)
  = (4 • 3) • (x3 • x2)
 =     12   •    x5   = 12x5		 Notice that the factors were regrouped and then multiplied.  Also, multiply powers with the same base by adding the exponents.
Example 2:
monomial • binomial
 = x2 + 4x		 This problem requires the distributive property.  You need to multiply each term in the parentheses by the monomial (distribute the x across the parentheses).
Example 3:
monomial • trinomial
 = 2x3 + 6x2 + 8x		 Notice the distributive property at work again.
Example 4:
monomial • polynomial
= 3x5 - 9x4 + 18x3 - 15x2 		Again, the distributive property is needed along with the rule for multiplying powers.


 

 If you are solving multiple choice questions, you can use the calculator to "check" your work with polynomials.
You can use a Numerical Checking process:  Numerical Process
                                  or
You can use an Equation Checking process::  Equation Process