# 9.3: Special Products of Polynomials

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.

## Vocabulary

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 and in the formulas.

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

Example:

*Square the binomial.*

Solution:

The minus sign tells us to use . Setting and (and not ),

## Error Troubleshooting

General Tip: Students commit a very common error when they write, for example, ; 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, .
- 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.

### Image Attributions

## Description

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## Tags:

Activities
Answer Key
Answers
(43 more)
Assessment
binomial
binomial formula
CK.MAT.ENG.TE.1.Algebra-I.9
coefficients
Common Misconceptions
Concept Check and Troubleshooting
constant
cubic term
degree
degree of polynomials
Differentiated Instruction
distributive property
Enrichment
factoring quadratic expressions
greatest common monomial factor
Inquiry Process
leading coefficient
leading term
linear term
monomial
Pacing
perfect square trinomial
polynomials
Problem Sets
Problem Solving
quadratic term
Quizzes
Science Inquiry
simplifying polynomials
Solution Key
Solutions
square of a binomial
standard form
Teacher Edition
Teaching Strategies
Teaching Strategies and Tips
term
Testing
Tests
trinomial
Worksheets
zero-product property

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## Date Created:

Feb 22, 2012## Last Modified:

Aug 22, 2014
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