MATHEMATICS 8 QUARTER 1 LESSON 2

1. MATHEMATICS 8
FACTORING THE
DIFFERENCE OF TWO
SQUARES
Ma’am Ehlmz

2. DRILL Rewrite each expression to the
power of two.
1) 4
2) a6
3) 16b2
4) 25x6
y4
5) 1
(2)2
(a3
)2
(4b)2
(5x3
y2
)2
(1)2

3. DRILL
What is a perfect square?
 A number that is the product of
two equal facors.
Examples:
1. 4 = 2 2 = 2
∙ 2
2. 16b2
= 4b2
4b
∙ 2
= 4b6
Thus, 4 and 16b2
are perfect square.

4. REVIEW Identify the polynomials that
have common monomial factor.
1) abc + abd
2) 24m2
– 12m
3) x2
– y2
4) 25 – b2
ab (c + d)
12m (m – 1)
No common
monomial factor
No common
monomial factor

5. MOTIVATION Think Deeper!
3) x2
– y2
4) 25 – b2
No common
monomial factor
No common
monomial factor
Is there other way
to factor
polynomials
in this form?

6. LESSON Factoring The Difference Of Two
Squares
For you to have a better understanding about this lesson,
observe how the expressions below are factored. Observe
how each term relates with each other.
a. x2
-y2
= (x+y)(x-y)
b. 4x2
-36 = (2x+6)(2x-6)
c. a2
b4
-81 = (ab2
-9)(ab2
+9)
d. 16b6
-25b2
= (4b3
-5b)(4a3
+5b)
e. - 2
n6
= (+ n3
)(- n3
)

7. ANALYSIS Factoring The Difference Of
Two Squares
1. What is the first term of each polynomial?
2. What is the last term of each polynomial?
3. What is the Middle term sign of each
polynomial?

8. ANALYSIS Factoring The Difference Of
Two Squares
4. How was the polynomial factored?
5. What pattern is seen in the factors of the
difference of two terms?
6. Can all expressions be factored using difference
of two squares? Why or why not

9. ANALYSIS Factoring The Difference Of
Two Squares
7. When can yu factor expressions using
difference of two squares?

10. ANALYSIS Factoring The Difference Of
Two Squares
The factors of the difference of two squares
are the sum and difference of the square
roots of the first and last terms.
x2
– y2
= ( x+ y ) ( x −y )
REMEMBER THIS!

11. ANALYSIS Factoring The Difference Of
Two Squares
REMEMBER THIS!
Example:
4x2
– 36y2
The square root of 4x2
is 2x and the
square root of 36y2
is 6y.
To write their factors, write the product of
the sum and difference of the square roots of
4x2
-36y2
, that is (2x-+6y)(2x-y)

12. YOUR TURN!
Match polynomials of column A to its
corresponding factors in column B.
Column A Column B
1. x2
– 16 a. (9 + m)(9 – m)
2. 9 - m2
b. (x – 3)(x + 3)
3. x2
– 4 c. (x + 4)(x – 4)
4. 81 - m2
d. (3 – m)(3 + m)
5. x2
– 9 e. (x + 2)(x – 2)

13. SUM UP!
Summarize the concept of factoring
polynomials with difference of two squares.
1) What are the factors of polynomials with
difference of two squares?
2) How to find the factors of a given
polynomial with difference of two squares?

14. ACTIVITY Write it in your activity
notebook.
Find the factors of the given polynomials.
1) c2
– 25
2) 4w4
– 1
3) 36 – 25h6
4) 49k4
– 100y6
5) 1 – 9p12
r10

15. ASSIGNMENT Write it in your activity
notebook.