What's the Formula for the Product of a Sum and a Difference?

Note:

Multiplying monomials like (a + b) and (a - b) is really important when it comes to factoring, so if you want to get good at factoring, you're going to have to understand how to multiply a sum like (a + b) with a difference like (a - b)!

Keywords:

definition
factoring
product
difference
foil
product of a sum and difference
polynomial
sum
multiply
expand
difference of squares
binomial

Background Tutorials

Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.
- What's a Term?
  
  Polynomials are those expressions that have variables raised to all sorts of powers and multiplied by all types of numbers. When you work with polynomials you need to know a bit of vocabulary, and one of the words you need to feel comfortable with is 'term'. So check out this tutorial, where you'll learn exactly what a 'term' in a polynomial is all about.
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
- What is a Variable?
  
  You can't do algebra without working with variables, but variables can be confusing. If you've ever wondered what variables are, then this tutorial is for you!
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
- How Do You Multiply Binomials Using FOIL?
  
  Looking for practice using the FOIL method? This tutorial delivers! It takes you step-by-step through the FOIL method as you multiply together to binomials.
- What's FOIL?
  
  The FOIL method. No, not aluminum foil! The FOIL method stands for First, Outer, Inner, and Last. It's a popular way multiply two binomials together. This tutorial makes the FOIL method a breeze!