9.6: Factoring Special Products
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
 quadratic polynomial equations
 double root
Teaching Strategies and Tips
Emphasize that students are reversing the specialproducts formulas introduced three lessons ago.
Have students use the vocabulary:

\begin{align*}a^2  b^2\end{align*}
a2−b2 is a difference of squares. 
\begin{align*}(a + b)(a  b)\end{align*}
(a+b)(a−b) is the product of a sum and difference. 
\begin{align*}a^2 + 2ab + b^2\end{align*}
a2+2ab+b2 and \begin{align*}a^2  2ab + b^2\end{align*}a2−2ab+b2 are perfect square trinomials. 
\begin{align*}(a + b)^2\end{align*}
(a+b)2 and \begin{align*}(a  b)^2\end{align*}(a−b)2 are squares of binomials.
The key to factoring special products is recognizing the special form, but also determining what \begin{align*}a\end{align*}
 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*}
Error Troubleshooting
General Tip: Remind students to check their solutions by substituting each in the original equation.
Review Question 8 is quadraticlike. Show students that \begin{align*}x^4 = (x^2)^2\end{align*}