# 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.

## 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.

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standard form
factoring quadratic expressions
perfect square trinomial
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CK.MAT.ENG.TE.1.Algebra-I.9

## Date Created:

Feb 22, 2012## Last Modified:

Aug 22, 2014
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