Online College Courses for Credit

3 Tutorials that teach Multiplying Polynomials
Take your pick:
Multiplying Polynomials

Multiplying Polynomials

Author: Sophia Tutorial

This lesson cover multiplying polynomials.

See More

Try Our College Algebra Course. For FREE.

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to many different colleges and universities.*

Begin Free Trial
No credit card required

29 Sophia partners guarantee credit transfer.

310 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 27 of Sophia’s online courses. Many different colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.


What's Covered

  • Distribution
  • FOIL
  • Multiplying Three Binomials 

Multiplying Polynomials


When multiplying two expressions, we can distribute all factors into each term of the other expression.  With simple algebraic expression, this typically involves a coefficient and a single variable, as in the example below:

We can also use the distribution property with examples involving other variables or exponents:


In the previous examples, we multiplied a monomial (single term expression) by a binomial (two term expression).  When multiplying two binomials together, we use a special case of the distributive rule, commonly referred to as FOIL.  FOIL stands for First, Outside, Inside, Last, and describes how to distribute all terms in binomial multiplication.  This is shown in the example below:


Multiplying Three Binomials

How can the distributive and FOIL processes be modified to multiply three binomials?  One strategy is to perform the steps in FOIL to two of the binomials, and then distribute the third binomial into the product revealed by FOIL.  This is illustrated in the example below:

So far, all that we have done is used FOIL to multiply two of the three binomials.  In order to multiply the third binomial, we will distribute each term in 2x – 1 into every term in x2 – 2x + 3.  In order to keep things organized, it is helpful to distribute separately, and then add the two new polynomials:

Our final step is two add the the polynomials after distributing 2x and –1.  Remember to use coefficients of 0 to keep the vertical alignment between like terms.