The document provides a lesson on factoring the sum and difference of two cubes. It begins with definitions of perfect cubes and examples of factoring expressions like x3 - 27 and x3 + 27 using the rule that (x - a)(x2 + ax + a2) = x3 - a3 and (x + a)(x2 - ax + a2) = x3 + a3. Students are then asked to determine if additional expressions are the sum or difference of two cubes and factor them accordingly. The next section covers factoring perfect square trinomials, defining them as expressions of the form a2 + 2ab + b2 and providing the factoring pattern (a + b)2. Examples

1. Q1 - Week 2
APPLE JEAN Y. ALAG
Math Class

2. Class Recap

3. Factoring
Polynomials

4. Greatest Common Monomial
Factoring

5. Factoring
Difference of Two Squares

6. Lesson For The Day
Lesson For The Day
FACTORING SUM
AND DIFFERENCE
OF TWO CUBES

7. Class Objectives
Class Objectives
Recall the concept of
perfect cube and
express mathematical
expression to the
power of 3.
OBJECTIVE 1 OBJECTIVE 2
Factor out sum and
difference of two
cubes.

8. Perfect cubes are numbers or
expressions that can be expressed to
the power of 3.
Concepts&
Definitions
1
8
27
64
125
216
343
x
y
a
3
6
9

9. Examples and Illustrations
EXAMPLE 1
27
EXAMPLE 2 EXAMPLE 3
64y
125x
3
3

10. Factoring
SumandDifferenceof
TwoCubes
Rule

11. Product:
Seethe
pattern
3
x - 27
Factored Form: (x - 3) (x + 3x +9)
2
Factored Form: (x + 3) (x - 3x +9)
Product: x + 27
3
2

12. Activity
Time 1
Determine whether the following
polynomials are sum of two cubes,
difference of two cubes, or neither.

13. Factoring
SumandDifferenceof
TwoCubes
Rule

14. Examples and Illustrations
EXAMPLE 1 EXAMPLE 2 EXAMPLE 3
8k + 1
a - 27
3
3
y + 8
3

15. Examples and Illustrations
EXAMPLE 4 EXAMPLE 5 EXAMPLE 6
5h + 8k
3
8x - 64
3

16. Activity
Time 2
Factor each completely.

17. youtube.com
WowMath
Grade 8 playlist for Quarter 1
AdditionalResources

18. POINT 1
POINT 3
POINT 2
Check if the given is
sum of two cubes or
difference of two cubes.
If yes, apply the rule or
pattern in factoring such
given. If not, apply first the
greatest common
monomial factoring.
ClassRecap

19. SEE YOU NEXT TIME
Thank You

20. Q1 - Week 2
APPLE JEAN Y. ALAG
Math Class

21. POINT 1
POINT 3
POINT 2
Check if the given is
sum of two cubes or
difference of two cubes.
If yes, apply the rule or
pattern in factoring such
given. If not, apply first the
greatest common
monomial factoring.
ClassRecap

22. Factoring
SumandDifferenceof
TwoCubes
Rule

23. Lesson For The Day
Lesson For The Day
FACTORING
PERFECT SQUARE
TRINOMIALS

24. first and last terms which are
perfect squares and;
the middle term is twice the
product of the first and last terms
Perfect Square Trinomial is the result
of squaring a binomial.
A perfect square trinomial has:
Concepts&
Definitions

25. Rule/Pattern

26. Activity
Time 1
Directions: Determine whether the given
expressions are perfect square trinomials.

27. Concepts&
Definitions
To factor the given trinomial:
1. Examine whether the first term and
last term are perfect squares.
2. Look at the middle term. Check
whether it is twice the product of the
square root of the first term and last
term.

28. Concepts&
Definitions
3. If conditions 1 and 2 were satisfied
then, the expression is a perfect square
trinomial.
4. Factor completely the given trinomial
following the pattern

29. Reminders
The steps given above are ONLY
applicable for perfect square trinomial.
If what is to be factored is NOT a
perfect square trinomial then other
possible techniques may be
applied.

30. Examples and Illustrations
EXAMPLE 1 EXAMPLE 2 EXAMPLE 3
4x + 4x + 1
x +14xy + 49 y
2
2
2
n + 16n + 64
2

31. Examples and Illustrations
EXAMPLE 4 EXAMPLE 5 EXAMPLE 6
4x + 4x + 1
x +14xy + 49 y
2
2
2
2
3x − 18xy + 27y
2