DDL IN MATH 8 WEEK 1

1. K to 12
DAILY LESSON LOG
School DEL CARMEN INTEGRATED HIGH SCHOOL Grade Level 8
Teacher AMY N. PONCE Learning Area MATHEMATICS
Teaching Dates & Time AUG. 29-31, SEP. 1-2, 2022 // 6:30 –7:20 / 7:20 – 8:10 / 8:10 – 9:00 Quarter 1ST
AUGUST 29 AUGUST 30 AUGUST 31 SEPTEMBER 1 SEPTEMBER 2
I. OBJECTIVES
1. Content Standards The learner demonstrates understanding of key concepts of factors of polynomials, rational algebraic expressions, linear equations, and inequalities in two
variables, systems of linear equations and inequalities in two variables and linear functions.
2. Performance Standards The learner is able to formulate real-life problems involving factors of polynomials, rational algebraic expressions, linear equations and inequalities in two
variables, systems of linear equations and inequalities in two variables and linear functions, and solve these problems accurately using a variety of strategies
3. Learning Competencies/
Objectives
Factors completely different types
of polynomials (polynomials with
common monomial factor,
difference of two squares, sum and
difference of two cubes, perfect
square trinomials and general
trinomials)
(M8AL-Ia-b-1)
a. Factor polynomials with
common monomial factor.
b. Apply the theorems in proving
inequalities in triangle.
c. Appreciate the concept about
factoring out the common factor
in polynomials.
Factors completely different
types of polynomials
(polynomials with common
monomial factor, difference of
two squares, sum and difference
of two cubes, perfect square
trinomials and general
trinomials)
(M8AL-Ia-b-1)
a. Factor the difference of two
squares.
b. Solve equations by factoring
the difference of
two squares.
c. Find pleasures in working with
numbers.
Factors completely different
types of polynomials
(polynomials with common
monomial factor, difference of
two squares, sum and difference
of two cubes, perfect square
trinomials and general
trinomials)
(M8AL-Ia-b-1)
a. Find the factors of the sum or
difference of two cubes.
b. Completely factor a
polynomial involving the
sum and difference of two
cubes.
c. Find pleasures in working with
numbers.
Factors completely different
types of polynomials
(polynomials with common
monomial factor, difference of
two squares, sum and difference
of two cubes, perfect square
trinomials and general
trinomials)
(M8AL-Ia-b-1)
a. Identify a perfect square
trinomial.
b. Get the square of the
numbers.
c. Factor a perfect square
trinomial.
II. CONTENT
NO CLASSES
(NATONAL HEROES
DAY)
Factor of Polynomials with
Common Monomial Factor
(CMF)
Factoring the Difference of
Two Squares
Factoring the Sum or
Difference of Two Cubes
Factoring a Perfect Square
Trinomial
III. LEARNING RESOURCES
A. References
1. Teacher’s Guide pages 29-33 pages 34-35 pages 36-37 pages 38-39

2. 2. Learner’s Materials pages 27-31 pages 32-33 pages 34-35 pages 36-38
3. Textbook Intermediate Algebra UBD pages
22-23
Mathematics Activity
Sourcebook pages 22-23
Mathematics Activity
Sourcebook pages 25- 26
Intermediate Algebra UBD pages
24-25
4. Additional Materials
from Learning
Resource (LR) portal
B. Other Learning
Resources
Grade 8 LCTG by Dep Ed Cavite
Mathematics 2016
laptop, LCD
Grade 8 LCTG by Dep Ed Cavite
Mathematics 2016
laptop, LCD
Grade 8 LCTG by Dep Ed Cavite
Mathematics 2016
laptop, LCD
Grade 8 LCTG by Dep Ed Cavite
Mathematics 2016
laptop, LCD
IV. PROCEDURES
A. Reviewing previous lesson
or presenting the new
lesson
1. Asking the common physical
features/ behavioral traits among
siblings in the family.
2. What are the things common to
each set of pictures?
SECRET MESSAGE
Find the square roots and solve
the secret message.
4 = ___ 16 = ___
16 = ___ 81 = ___
49 = ___ 9 = ___
81 = ___ 25 = ___
16 = ___ 100 = ___
9 = ___ 36 = ___
121= ___ 16 = ___
25 = ___ 9 = ___
144 = ___ 64 = ___
81= ___ 289 = ___
225 = ___ 49 =___
9 = ___ 81 = ___
25= ___ 16 =___
100= ___ 9 =___
A B C D
16 16 25 1000
E F G H
299 100 400 4
Purpose Setting Activity
So here are the formulas that
summarize how to factor the
sum and difference of two
cubes.
Study them carefully using the
following diagrams.
Find the square of the following:
1. 1 6. 36
2. 4 7. 49
3. 9 8. 81
4. 16 9. a2
5. 25 10. x4

3. I J K L
36 81 64 81
M N O P
144 100 9 64
Q R S T
49 900 121 4
U V W X
24 9 81 225
Y X
8 9
Observations:
•For the “sum” case, the
binomial factor on the right side
of the equation has a middle
sign that is positive.
•In addition to the “sum” case,
the middle sign of the trinomial
factor will always be opposite
the middle sign of the given
problem. Therefore, it is
negative.
•For the “difference” case, the
binomial factor on the right side
of the equation has a middle
sign that is negative.
•In addition to the “difference”
case, the middle sign of the
trinomial factor will always be
opposite the middle sign of the
given problem. Therefore, it is
positive.
B. Establishing a purpose for
the lesson
Factoring the common monomial
factor is the reverse process of
monomial to polynomials.
a (b + c) = ab + ac
Factoring the difference of two
squares is the reverse process of
the product of sum and
difference of two terms.
(x + y) (x – y) = x2
– y2
Factoring the sum or difference
of two cubes is the reverse
process of product of binomial
and trinomial.
(x + y) (x2
– xy + y2
)
Factoring a perfect square
trinomial is the reverse process
of square o binomial.
(x + y)2
= x2
+ 2xy + y2
(x - y)2
= x2
- 2xy + y2

4. = x3
+ y3
(x + y) (x2
+ xy + y2
)
= x3
- y3
C. Presenting examples/
instances of the lesson
a. Factor xy +xz
Get the CMF: x
Divide xy + xz by x
Quotient: y + z
Thus, xy + xz = x(y + z)
b. Factor 5n² + 15n
Get the CMF, 5n
Divide 5n² = 15 n by 5n
Quotient: n + 3
Thus, 5n² + 15n
= 5n (n + 3)
c. Factor 27y² + 9y -18
The CMF is 9
Divide 27y² + 9y -18 by 9
The quotient is 3y² + y -2
Thus,27y² + 9y -18
= 9 (3y² + y -2)
Factor 4y2
- 36y6
•There is a common factor of
4y2
that can be factored out first
in this problem, to make the
problem easier.
4y2
(1 - 9y4
)
•In the factor (1 - 9y4
), 1 and 9y4
are perfect squares (their
coefficients are perfect squares,
and their exponents are even
numbers).
Since subtraction is occurring
between these squares, this
expression is the difference of
two squares.
•What times itself will give 1?
•What times itself will give 9y4
?
•The factors are (1 + 3y2
) and (1
- 3y2
).
•Answer:
4y2
(1 + 3y2
) (1 - 3y2
) or
4y2
(1 - 3y2
) (1 + 3y2
)
1: Factor x3
+ 27
Currently the problem is not
written in the form that we want.
Each term must be written as
cube, that is, an expression
raised to a power of 3. The term
with variable x is okay but the 27
should be taken care of.
Obviously, we know that 27 =
(3)(3)(3) = 33
.
Rewrite the original problem as
sum of two cubes, and then
simplify. Since this is the "sum"
case, the binomial factor and
trinomial factor will have positive
and negative middle signs,
respectively.
x3
+ 27 = (x)3
+ (3)3
= (x+3) [{x)2
–(x)(3) +(3)2
]
=(x+3) (x2
-3x+9)
Example 2: Factor y3
- 8
This is a case of difference of
two cubes since the number 8
can be written as a cube of a
number, where 8 = (2)(2)(2) = 23
.
Apply the rule for difference of
two cubes and simplify. Since
this is the "difference" case, the
binomial factor and trinomial
factor will have negative and
positive middle signs,
respectively.
Study the trinomials and their
corresponding binomial factors.
1. x2
+ 10x + 25 = (x + 5)2
2. 49x2
– 42 + 9
= (7x – 3)2
3. 36 + 20 m + 16m2
= (6 + 4m)2
4. 64x2
– 32xy + 4y2
= (8x – 2y)2
a. Relate the first term in the
trinomial to the first term in
the binomial factors.
b. Compare the second term in
the trinomial factor and the
sum of the product of the
inner terms and outer terms
of the binomials.
c. Observe the third term in the
trinomial and the product of
the second terms in the
binomials.

5. D. Discussing new concepts
and practicing new skills #
1
Question: What fruit is the main
product of Tagaytay City? You will
match the products in Column A
with the factors in Column B to
decode the answer.
Factor each of the following:
1. c² - d²
2. 1 - a²
3. (a + b)² - 4c²
4. 16x² - 4
5. a²b² - 144
Factor the following:
1. x3
– 8
2. 27x3
+ 1
3. x3
y6
– 64
4. m³ + 125
5. x³ + 343
Supply the missing term to make
a true statement.
1. m2
+ 12m + 36
= (m + ___)2
2. 16d2
– 24d + 9
= (4d – ___)2
3. a4
b2
– 6abc + 9c2
= (a2
b ___)2
4. 9n2
+ 30nd + 25d2
= (____ 5d)2
5. 49g2
– 84g +36
= (______)2
E. Discussing new concepts
and practicing new skills
#2
Factor the following
1. a²bc + ab²c + abc²
2. 4m²n² - 4mn³
3. 25a + 25b
Fill in the blanks to make the
sides of each equation
equivalent.
1. (_____) (x – 9)
= x² -81
2. (20 + 4) (_____)
= 20² -4²
3. (_____) (2a +3)
= 4a² - 9
Complete the factoring.
1. t3 - w3
= (t – w) ( )
2. m3 + n3
= (m + n) ( )
3. x3 + 8
= (x + 2) ( )
Factor the following trinomials.
1. x2
+ 4x + 4
2. x2
- 18x + 81
3. 4a2
+ 4a + 1
F. Developing mastery
(Leads to Formative
Assessment 3)
Factor the following:
1. 10x + 10y + 10z
2. bx + by + bz
3. 3x³ + 6x² + 9x
Factorize the following by taking
the difference of squares:
1. x2
– 100
2. a2
– 4
3. ab2
– 25
Factor each completely.
1. x ³ + 125
2. a ³ + 64
3. x ³ – 64
Factor the following:
1. 1. x2
– 5x + 25
2. 2. b2
-10b + 100
3. 36b2
– 12b + 1
G. Finding practical
applications of concepts
and skills in daily living
Factor the following
1. 16a² + 12a
2. 12am + 6a²m
3. 72x² + 36xy – 27x
Factor the following.
1. 100a2
– 25b2
2. 1 – 9a2
3. 81x2
– 1
Directions. Find the cube roots.
Then, match each solution to the
numbers at the bottom of the
page. Write the corresponding
letter in each blank to the
question. In the survey, Best
place for family picnic in
Tagaytay City?
No 1 2 3 4
27 512 343 216
Complete the perfect square
trinomial and factor them.
1. ___ + 16x + 64
2. x2
- ___ + 49
3. x2
+ 4x + ___

6. C R G O
9 10 11
1331 1000 219
I C V
12 13 14
0 64 125
0 E N
12 11 3 5 9
10 7 8 6 13
4
5 6 7 8
1728 8 1 729
P 2 1 1
H. Making generalizations
and abstractions about the
lesson
Common Monomial Factor
To factor polynomial with
common monomial factor,
expressed the given polynomial as
a product of the common
monomial factor and the quotient
obtained when the given
polynomial is divided by the
common monomial factor.
The factors of the difference of
two squares are the sum of the
square roots of the first and
second terms times the
difference of their square roots.
*The factors of 𝑎2
− 𝑏2
= 𝑎𝑟𝑒 ( 𝑎 + 𝑏 ) 𝑎𝑛𝑑 ( 𝑎 −𝑏 ).
1. The sum of the cubes of two
terms is equal to the sum
of the two terms multiplied
by the sum of the squares of
these terms minus the
product of these two terms.
a³ + b³
= (a + b (a² - ab + b²)
2. The difference of the cubes of
two terms is equal to the
difference of the two terms
multiplied by the sum of the
squares of these two terms
In factoring a perfect square
trinomial, the following should
be noted:
1. The factors are binomials with
like terms
wherein the terms are the
square roots of the first and
the last terms of the
trinomial.
2. The sign connecting the
terms of the binomial
factor is the same as
the sign of the middle
term of the trinomial.

7. plus the product of these two
terms.
a³ - b³
= (a - b (a² + ab + b²)
I. Evaluating learning Factor the following:
1. 5x + 5y + 5z
2. ax + ay + az
3. 4x³ + 8x² + 12x
4. 6x + 18y – 9z
5. 3a³ + 6a² + 12
Factorize the following by taking
the difference of squares:
1. x2
– 9
2. a2
– 1
3. ab2
– 16
4. 16𝑥2
– 49
5. 54𝑥2
– 6y2
Supply the missing expression.
1. 𝑚3
- 27
= (m – 3) _________
2. 64 + 27𝑛3
= ____ (16 – 12n + 9𝑛2
)
3. _______
= (2p + 5q) (4𝑝2
– 10pq + 25𝑞2
)
4. 𝑥6
+ 1000
= _____𝑥4
- 10𝑥2
+ 100)
5. ________
= (6x – 7y) (36𝑥2
+ 42xy + 49𝑦2
)
Factor the following:
3. 1. x2
– 6x + 9
4. 2. b2
-12b + 36
3. 4b2
– 4b + 1
4. 49p2
– 56p = 16
5. 49k2
– 28kp + 4p2
J. Additional activities for
application or remediation
Study Factoring Polynomials
1. What is a common monomial
factor?
2. How will you factor polynomial
by grouping?
Reference: G8 Mathematics
Learner’s Module pages 45-46
Factorize the following by taking
the difference of squares:
1. x2
– 9
2. a2
– 1
3. ab2
– 16
Solve the following:
1. The product of two
consecutive even integers is
528. Find the value of each
integer.
Complete the perfect square
trinomial and factor them.
1. ___ + 16x + 64
2. x2
- ___ + 49
3. x2
+ 4x + ___
V. REMARKS
NO CLASSES
(NATONAL HEROES
DAY)
VI. REFLECTION

8. 1. No. of learners who earned 80% on
the formative assessment
2. No. of learners who require
additional activities for
remediation.
3. Did the remedial lessons work? No.
of learners who have caught up
with the lesson.
4. No. of learners who continue to
require remediation
5. Which of my teaching strategies
worked well? Why did this work?
6. What difficulties did I encounter
which my principal or supervisor
can help me solve?
Prepared by: Checked by:
Amy N. Ponce Mary Jane P. MallarI
Teacher I Principal I