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 .

Guiding Questions:

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
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?

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

Notes for Teachers:

Be patient when letting students identify the patterns in these problems. It is better if they can discover on their own, as opposed to just giving them the results.

Video of the Day:

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

7.4.2 Some Perfect Square Trinomials

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

7.4.2 Factoring Some Trinomials.mp4

Exercises and Problems:

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

Online Sources:

Khan Academy: Factoring Perfect Squares

Additional Resource for Teachers:

If you wish to download the contents of this page as a printable pdf, click here: 7.4 Difference of Two Squares.pdf