7.4 - The Difference of Two Squares and Some Perfect Square Trinomials

Introduction:

This is a set of guiding questions and materials for creating your own lesson plan on factoring the difference of two squares and some perfect square trinomials.

 Common Core State Standards:

A.SSE.2

 Learning Objectives:

• To factor the difference of two squares.
• To factor trinomials of the form x 2 + 2ax + a 2 = (x + a) 2 .

• What do you notice in these four products?
• (x + 1)(x – 1)
• (x + 2)(x – 2)
• (x + 3)(x – 3)
• (x + 4)(x – 4)
• What is $x^{2^{^{ }}}-25$
• What about $9x^2-4?$
• What do both terms have in common?
• What should we call this process?
• The difference of two perfect squares: $x^2-b^2=\left(x+b\right)\left(x-b\right)$
• Does this property hold if we change to addition the operation in the second factor?
• What is (x + 1)(x + 1)?
• What is (x + 2)(x + 2)?
• What is (x + 3)(x + 3)?
• What can we infer?
• $\left(x+a\right)^2=x^2+2ax+a^2$

7.4.1 The Difference of Two Squares

We factor the difference of two perfect squares.

7.4.1 The Difference of Two Squares.mp4 Download 7.4.1 The Difference of Two Squares.mp4Play media comment. 

7.4.2 Some Perfect Square Trinomials

$\left(x+a\right)^2=x^2+2ax+a^2$

 7.4.2 Factoring Some Trinomials.mp4 Download 7.4.2 Factoring Some Trinomials.mp4Play media comment.

• North Carolina Common Core Math 1 Item Bank, Nagy-Lup, p.18
• Factor $\left(x-3\right)^2-16$

• Khan Academy: Factoring Perfect Squares Links to an external site.