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9.6: Factoring Special Products

Difficulty Level: At Grade 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:

• \begin{align*}a^2 - b^2\end{align*} is a difference of squares.
• \begin{align*}(a + b)(a - b)\end{align*} is the product of a sum and difference.
• \begin{align*}a^2 + 2ab + b^2\end{align*} and \begin{align*}a^2 - 2ab + b^2\end{align*} are perfect square trinomials.
• \begin{align*}(a + b)^2\end{align*} and \begin{align*}(a - b)^2\end{align*} are squares of binomials.

The key to factoring special products is recognizing the special form, but also determining what \begin{align*}a\end{align*} and \begin{align*}b\end{align*} 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 \begin{align*}-1\end{align*} 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 \begin{align*}x^4 = (x^2)^2\end{align*}.

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