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.
Terms introduced in this lesson:
recognizing special product
factoring perfect square trinomials
quadratic polynomial equations
Teaching Strategies and Tips
Emphasize that students are reversing the special-products formulas introduced three lessons ago.
Have students use the vocabulary:
a2−b2 is a difference of squares.
(a+b)(a−b) is the product of a sum and difference.
a2+2ab+b2 and a2−2ab+b2 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.
General Tip: Remind students to check their solutions by substituting each in the original equation.
Review Question 8 is quadratic-like. Show students that x4=(x2)2.