<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Skip Navigation
Our Terms of Use (click here to view) and Privacy Policy (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use and Privacy Policy.

9.3: Special Products of Polynomials

Difficulty Level: At Grade Created by: CK-12

Learning Objectives

At the end of this lesson, students will be able to:

  • Find the square of a binomial.
  • Find the product of binomials using sum and difference formula.
  • Solve problems using special products of polynomials.


Terms introduced in this lesson:

second-degree trinomial
square of a binomial, binomial square
sum and difference of terms
difference of squares

Teaching Strategies and Tips

In this lesson, students learn about special products of binomials.

  • Have students learn to recognize the basic patterns.
  • In classroom examples, use colors to denote the numbers playing the role of a and b in the formulas.

In the special formulas, point out that b is considered positive; the sign does not go with the term.


Square the binomial.



The minus sign tells us to use (ab)2=a22ab+b2. Setting a=x and b=3 (and not 3),


Error Troubleshooting

General Tip: Students commit a very common error when they write, for example, (x+y)2=x2+y2; that is, they distribute the exponent over addition instead of multiplication.

  • The power rule for products does not apply to sums or differences within the parentheses. In general, (xn+ym)pxnp+ymp.
  • Students can learn to avoid this mistake by recalling the exponent definition. Therefore, a polynomial raised to an exponent means that the polynomial is multiplied by itself as many times as the exponent indicates. For example:


  • See Review Questions 1-4, especially Problem 4.

My Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Show More

Image Attributions

Show Hide Details
Files can only be attached to the latest version of section
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original