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9.6: Factoring Special Products

Created by: CK-12

Learning Objectives

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

• Factor the difference of two squares.
• Factor perfect square trinomials.
• Solve quadratic polynomial equation by factoring.

Vocabulary

Terms introduced in this lesson:

recognizing special product
factoring perfect square trinomials
double root

Teaching Strategies and Tips

Emphasize that students are reversing the special-products formulas introduced three lessons ago.

Have students use the vocabulary:

• $a^2 - b^2$ is a difference of squares.
• $(a + b)(a - b)$ is the product of a sum and difference.
• $a^2 + 2ab + b^2$ and $a^2 - 2ab + b^2$ are perfect square trinomials.
• $(a + b)^2$ and $(a - b)^2$ are squares of binomials.

The key to factoring special products is recognizing the special form, but also determining what $a$ and $b$ are.

• Recognizing perfect integer squares, for example, may be difficult to some students. Suggest that students break numbers down into prime factorization first. See Example 2.

Remind students to pull out $-1$ and/or the GCF in a polynomial before attempting to factor it. This simplifies the task dramatically.

Error Troubleshooting

General Tip: Remind students to check their solutions by substituting each in the original equation.

Review Question 8 is quadratic-like. Show students that $x^4 = (x^2)^2$.

Date Created:

Feb 22, 2012

Apr 29, 2014
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