This document discusses factoring polynomials that are the difference of two squares using the formula a2 - b2 = (a + b)(a - b). It provides examples of factoring polynomials like x2 - 16, 9x2 - 100, and 36m2 - 49n4. It also lists 10 practice problems for factoring polynomials that are differences of two squares and references where readers can learn more.

1. FACTORS OF
POLYNOMIALS
Factoring the Difference
of Two Squares

2. Jessebel G. Bautista
Antonio J. Villegas Voc’l High School
My
Profile

3. OBJECTIVES
• Identify the perfect squares
• Factor the difference of two squares
• Factor with accuracy

4. Factoring a polynomial involves writing
it as a product of two or more
polynomials. It reverses the process of
polynomial multiplication.
Every polynomial that is a difference of squares can
be factored by applying the following formula:
a2 – b2 = (a + b) (a – b)

5. Every polynomial that is a
difference of squares can be
factored by applying the
following formula:
a2 – b2 = (a + b) (a – b)
Note that a and b in the pattern
can be any algebraic expression.
For example, for a = x , and b=2
we get the following:
x2 – 22 = (x – 2) (x + 2)
The polynomial x2 – 4 is now expressed in factored form, (x+2)(x−2).
We can expand the right-hand side of this equation to justify the
factorization:
(x + 2) (x – 2) = x(x – 2) + 2(x – 2)
= x2 – 2x + 2x – 4
= x2 – 4
Now that we understand the pattern, let's use it to factor a few more
polynomials.

6. Both x2 and 16 are perfect square since x2 = (x)2 and 16 = (4)2. In other
words.
x2 – 16 = (x)2 – (4)2
EXAMPLE 1: Factoring x2 - 16
Since the two squares are being subtracted, we can see that this
polynomial represents a difference of squares. We can use
the difference of squares pattern to factor this expression:
a2 – b2 = (a + b) (a – b)
In our case, a = x and b = 4. Therefore, our polynomial factors as
follows:
(x)2 – (4)2 = (x – 4) (x + 4)
We can check our work by ensuring the product of these two factors is
x2 – 16 .

7. Both 9x2 and 100 are perfect square since 9x2 = (3x)2 and 100 = (10)2.
In other words.
9x2 – 100 = (3x)2 – (10)2
EXAMPLE 2: Factoring 9x2 - 100
Since the two squares are being subtracted, we can see that this
polynomial represents a difference of squares. We can use
the difference of squares pattern to factor this expression:
a2 – b2 = (a + b) (a – b)
In our case, a = 3x and b = 10. Therefore, our polynomial factors as
follows:
(3x)2 – (10)2 = (3x – 10) (3x + 10)
We can check our work by ensuring the product of these two factors is
9x2 – 100 .

8. Both 36m2 and 49n4 are perfect square since 36m2 = (6m)2 and
49n4 = (7n2)2. In other words.
36m2 – 49n4 = (6m)2 – (7n2)2
EXAMPLE 3: Factoring 36m2 – 49n4
Since the two squares are being subtracted, we can see that this
polynomial represents a difference of squares. We can use
the difference of squares pattern to factor this expression:
a2 – b2 = (a + b) (a – b)
In our case, a = 6m and b = 7n2. Therefore, our polynomial factors as
follows:
(6m)2 – (7n2)2 = (6m – 7n2) (6m + 7n2)
We can check our work by ensuring the product of these two factors is
36m2 – 49n4 .

9. 1. 4x2 – 25
2. 9y2 – 100
3. 49m2 – 121n2
4. 144 – 16n2
5. m2n2 – 196
TO DO …
Factor the following:
6. 169a2 – b2c2
7. 9x2 – 81
8. 289m2 – 256n2
9. 16b2 – 9c2
10. 121c4 – 169d2

10. REFERENCES:
https://www.khanacademy.org/math/algebra/x2f8bb11
595b61c86:quadratics-multiplying-
factoring/x2f8bb11595b61c86:factor-difference-
squares/a/factoring-quadratics-difference-of-squares
Grade 8 Math Time
k-to-12-grade-8-math-learner-module