Check:

(x + 5)(x – 5) Factored Form x2 + 5x – 5x – 25 Zero Pair x2 – 25 Simplified Form

Pre-Algebra

Essential Question: How do we factor a binomial that is a difference of two perfect squares?

Lesson Summary

Factoring a binomial that is a difference of two perfect squares

Step 1: Identify the polynomial as D.O.T.S

The polynomial must be a ….

binomial

difference of two perfect square terms Step 2: Take the square root of each term.

Step 3: Create 2 sets of parentheses (a sum and a difference). ( + )( – )

Step 4: Place the square root of each term inside the parentheses.

Step 5: Check by multiplying the binomial factors (double distribute).

Before reviewing the lesson and completing the practice problem set, watch the VIDEO!

The factored form of x2 – 25 is

(x + 5)(x – 5)

Difference

Of

Two

Squares

Factored Form: (x + 4)(x – 4) Does this product result in our original problem x2 – 16? Double distribute to find out. (x + 4)(x – 4) x2 – 4x + 4x – 16 Zero Pair

x2 – 16

Examples

Ex 1: Factor x2 – 16

1) Is it D.O.T.S ? Yes, it is a binomial difference of two perfect squares.

2) Take the square root of each term. = x and = 4

3) Create two sets of parentheses(sum and difference). ( + )( – ) 4) Place the square root of each term inside the ( ). (x + 4)(x – 4)

The factored form of x2 – 16 is (x + 4)(x – 4)

5) Check your work!

Perfect Square Terms:

x2 , 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225 …

Ex 2: Factor 49x2 – 121

( + )( - )

Factored Form: (7x + 11)(7x – 11)

Ex 3: Which polynomials below are D.O.T.S (a difference of two perfect squares)?

A) x2 – 2 NOT D.O.T.S: 2 is not a perfect square term x2 – 2

B) x – 100 NOT D.O.T.S: x is not a perfect square term x – 100

C) x2 + 25 NOT D.O.T.S: The binomial is not a difference, it’s a sum x2 + 25

D) x2 + 4x – 16 NOT D.O.T.S: The polynomial is not a binomial, it’s a trinomial

E) x2 – 36 YES!! IT’S D.O.T.S: A binomial that is a difference of two perfect squares

Practice Problem Set

ATTENTION ALL PRE-ALGEBRA STUENTS: We want to remind you that you and your peers create a learning community. We encourage you to face time, text or use any other appropriate communication to reach out to a friend and discuss your answers to the following questions. Working together and having meaningful mathematical discussions aids in your understanding of the subject matter.

Factor each binomial. 1. x2 – 1 2. x2 – 144 3. x2 – 100 4. 9x2 – 64 5. 4x2 – 81 6. 16x2 – 25

7. Determine if the polynomial expression below is D.O.T.S. Explain your reasoning.

a) x2 – 400 b) 36x2 + 1

c) x2 – 20 d) 25x2 – 4