Republic of the Philippines

Commission on Higher Education

Region IV-A CALABARZON
Kolehiyo ng Lungsod ng Lipa
College of Teacher Education
Marawoy, Lipa City

A Detailed Lesson Plan in Algebra

I. LEARNING COMPETENCIES

● Content Standards
The learner demonstrates understanding of key concepts of factoring
polynomials of the form ax4 + bx2y2 + cy4.
● Performance Standards
The learner is able to formulate and solve accurately problem
involving factoring polynomials of the form ax4 + bx2y2 + cy4.
● Learning Objectives
At the end of the lesson, the students are able to:
1. identify the key concepts of factoring polynomials of the form ax4 +
bx2y2 + cy4;
2. solve problems involving accurately;
3. relate factoring polynomials in real life situations.

II. SUBJECT MATTER

A. Topic: Factoring Polynomials of the form ax4 + bx2y2 + cy4.
B. References: College Algebra
https://openstax.org/details/books/college-algebra-2e
C. Materials: Marker, Whiteboard, LED Television, Laptop, PowerPoint Presentation,
and Cartolina.

III. LESSON PROPER

Teacher’s Activity Student’s Activity

A. Preliminary Activities

1. Prayer
Class, before we formally start with our
lesson this afternoon may I request
everyone to please stand and let us pray.

“Lord, bless each and every student

 here, as well as our teacher, as we
embark on another day of learning.
Please give us clear minds and open
hearts so we can grasp the knowledge
and lessons set before us. Help us to
be attentive, and let Your wisdom
guide us in our studies. Amen”

Before you take your seats, please

arrange your chairs properly and kindly
pick up those pieces of paper under your
chairs.

2. Greetings
Good afternoon, Class!!

I am Darlene Natal and I will be your

demonstrator for this afternoon.

Good afternoon, Ma’am!

Before we start, let me remind you our

factor rules.

All together please read.

FACTOR RULES

F-ollow the teacher’s directions the first

time they are given.

A-ctively participate in classroom

activities.

C-ompeting with oneself instead of

others.

T-reat others the way you want to be

treated.

O-pen up your mind to learn new

things.

R-aise your hand if you would like to

speak.
Thank you, is it clear class?
 Ask the teacher
politely for
clarificat
Raise your
hand if you
want to
answer.
c. Do not talk
with your
seatmate if
discussion is
going
Yes, Ma’am.

3. Checking of Attendance
For the attendance, Mr. Secretary, do we
have any absentees for today?
Secretary of the class: I’m glad to
report that no one is absent for today.

Thank you so much, Mr. Secretary.

B. Developmental Activities

1. Motivation
Before we start, I have prepared an
activity entitled “GHOST WHO”.
Kindly read the mechanics altogether.
Mechanics:
 Move your chairs on the side,
and the students will form a
circle in the middle.
 The students will count numbers
 1-19, and the teacher will draw
a number from the box.
 The student who got the same
number with the teacher will be
the ghost hunter.
 The teacher will present the 4
characters with their
corresponding sounds and
songs.
 The ghost hunter will choose a
character, and the students will
start moving around while
singing the song.
 When the students finished
singing, the one who will be
pointed out will portrait the
sound of the chosen character
and the ghost hunter will guess
who makes the sound.
Characters and their sounds
1. Monster – RAWRRRRR!!
2. Pirate – YOHOHOHO!!
3. Ghost – WOOOOOOH!! `
4. Ballerina – 1, 2,3! 1,2,3!!
Songs for:

1.“knock, knock, trick or treat? Who are

you? I’m a monster, I’m a monster”
2. “knock, knock, trick or treat? Who are
you? I’m a pirate, I’m a pirate”
3. “knock, knock, trick or treat? Who are
you? I’m a ghost, I’m a ghost”
4. “knock, knock, trick or treat? Who are
you? I’m a ballerina, I’m a ballerina”

Are the mechanics clear?

Yes Ma’am!
 (The students will play the game)

2. Activity
Let’s have another activity entitled
“Body and Soul”
I will be grouping you into 2 groups.

Now everyone, please read the

Mechanics.

Mechanics:
 The teacher will provide
different terms.
 Each group must select a
combination as many as they
can that, upon multiplication,
results an exponent of 4.
 You only have 3 minutes to
finish this activity.
 The team that will finish it first
will be able to have a treat.

Understood class?

Yes Ma’am.
(Timer’s start)

(Students play the game)

(After 3 minutes)
Time’s up!

(Students posting their works)

Congratulations team __________. Here is
your treat.

3. Analysis
a. How did you find the activity?
(Answer may vary)

b. Based on the activity, what do you

think will be our topic for today?
I think our topic for today is about
Factoring Polynomials.
Very Good!
Our topic for today is about Factoring
Polynomials of the form ax4 + bx2y2 + cy4.

But before that, let us first define what

is factoring polynomials.

Please read all boys.

Factoring a polynomial is expressing

the polynomial as a product of two or
more factors.
Alright thank you!

It is somewhat the reverse process of

multiplying.

To factor polynomial of the form ax4 +

bx2y2 + cy4, we need to rewrite them in the
form a2 – b2 by doing some manipulations
like adding and subtracting of other terms
as shown in our following examples.

Examples:
1. x4 – 13x2 + 36
a. √ x4 = x2
√ 36 = 6
b. (x2 - 6)2 = (x4 - 12x2 + 36) – x2
= (x2 - 6)2 – x2
= [(x2 - 6) + x] [(x2 - 6) - x]
= (x2 + x – 6) (x2 - x – 6)
= (x + 3) (x – 2) (x - 3) (x + 2)

2. 36x4 – 37x2 +1
a. √ 36x4 = 6x2
√1 = 1
b. (6x2 – 1)2 = (36x4 – 12x2 +1) – 25x2
 = (6x2 – 1)2 – 25x2
= [(6x2 - 1) + 5x] [(6x2 - 1) - 5x]
= (6x2 + 5x – 1) (6x2 - 5x – 1)
= (6x - 1) (x + 1) (6x + 1) (x –
1)

3. 4m4 + n4
a. √ 4 m4 = 2m2
√ n4 = n2
b. (2m2 + n2)2 = (4m4 + 4m2n2 + n4) - 4m2n2
= (2m2 + n2)2 - 4m2n2
= [(2m2 + n2) + 2mn] [(2m2 + n2) - 2mn]
= (2m2 + 2mn + n2) (2m2 – 2mn +
n2)

Can you follow class?

Yes ma’am.
Another examples:

4. 9x4 – 37x2 + 4
4. a. √ 9x4 = 3x2
√4 = 2
b. (3x2 – 2)2 = (9x4 – 12x2 +4) – 25x2
= (3x2 – 2)2 – 25x2
= [(3x 2 - 2) + 5x] [(3x2 - 2) -
5x]
= (3x 2 + 5x – 2) (3x2 - 5x –
2)
= (3x - 1) (x + 2) (3x + 1) (x –
5. 25x4 – 26x2 + 1 2)

5. a. √ 25x4 = 5x2
√1 = 1
b. (5x2 – 1)2 = (25x4 – 10x2 +1) – 16x2
= (5x2 – 1)2 – 16x2
= [(5x 2 - 1) + 4x] [(5x2 - 1) -
4x]
= (5x 2 + 4x – 1) (5x2 - 4x –
Very good class. 1)
Do you have any questions or = (5x - 1) (x + 1) (5x + 1) (x –
clarifications? 1)
 None Ma’am.

3. Abstraction
Let us see if you fully understand the
lesson.

1. What is factoring polynomials?

Factoring a polynomial is expressing
the polynomial as a product of two or
more factors.

2. In what form of polynomials, we are

trying to factor in our discussion?

In the form of ax4 + bx2y2 + cy4.

3. How can we factor polynomials in

the form of ax4 + bx2y2 + cy4? We need to rewrite them in the form
a2 – b2 by doing some manipulations
like adding and subtracting of other
terms.
Excellent!
It seems that you really understand our
lesson.
1. Application
For your next activity, it is entitled
“BOO FACTOR”.

Mechanics:

 With the same group, you need

to factor the given equation.
 You only have 5 minutes to
factor each.
 The group that has the highest
score will receive a treat.

1. a4 – 10a2 + 9

2. 4x4 – 17x2 + 4
3. 36p4 – (q – 1)2

4. m4 – 5m2 + 4

5. 64x⁴ + y4
Expected Answer:

1. a. √ a4 = a2
√9 = 3
b. (a2 – 3)2 = (a4 – 6a2 +9) – 4a2
= (a2 – 3)2 – 4x2
= [(a 2 - 3) + 2a] [(a2 - 3) –
2a]
= (a 2 + 2a – 3) (a2 – 2a –
3)
= (a + 3) (a - 1) (a - 3) (a +
1)
2. a. √ 4x4 = 2x2
√4 = 2
b. (2x2 – 2)2 = (4x4 – 8x2 +4) – 9x2
= (2x2 – 2)2 – 9x2
= [(2x 2 - 2) + 3x] [(2x2 - 2) -
3x]
= (2x 2 + 3x – 2) (2x2 - 3x –
2)
= (2x - 1) (x + 2) (2x + 1) (x –
2)
3. a. √ 36p4 = 6p2

√ (q – 1)2 = (q – 1)

b. [6p2 – (q – 1)]2

= (6p2 + (q – 1)) (6p2 - (q – 1)

= (6p2 + q – 1) (6p2 - q + 1)

4. a. √ m4 = m2
√4 = 2
b. (m2 – 2)2 = (m4 – 4m2 +4) – m2
= (m2 – 2)2 – m2
= [(m2 - 2) + m] [(m2 - 2) –
m]
= (m 2 + m – 2) (m2 – m –
2)
= (m + 2) (m - 1) (m - 2) (m +
1)

5. a. √ 64x4= 8x2
 √ y4 = y2
b. (8x2 + y2)2
= (64x4 + 16x2y2 + y4) – 16x2y2
= (8x2 + y2)2 – 16x2y2
= [(8x 2 + y2) + 4xy] [(8x2 + y2) –
4xy]
= (8x2 + 4xy + y2) (8x2 – 4xy +
y2)

2. Values Integration
Before we proceed to your quiz,
kindly take a look at the picture.

What can you say about this picture?

Anyone from the class?

(Answer may vary)

Thank you, ______________.

As we can see in the illustration, all of us

have dreams to reach. In reaching our
main goals, there will always hindrances
for us to face. The simplest thing to do is to
factor out those things that can stop us
from dreaming. As a result, we can now
move and claim the success that we are
aiming and realize that we can make it this
far. As we reflect it to our lesson, factoring
is a trial-and-error process where we can
experience some errors in finding factors.
The thing that we can do is to continue and
move forward until we can come up with
the right answer or factor though it
sometimes hard but keep believing in
ourself that we can do it.

Now, it seems you would be able to

understand and apply the lesson from our
journey. Let’s have your evaluation.

1. Evaluation
Directions: On a one whole sheet of
yellow paper. For 10 minutes, find the
factors of the given polynomial. Show
your complete solution.
1. 16k4 – 17k2 + 1
2. 9w4 – 37w2 + 4

3. 64a⁴ + b4
4. 49v4 – (z– 1)2

Answers:
1. a. √ 16k4 = 4k2
√1 = 1
b. (4k2 – 1)2 = (16k4 – 8k2 +1) – 9k2
= (4k2 – 1)2 – 9k2
= [(4k 2 - 1) + 3k] [(4k2 - 1) –
3k]
= (4k 2 + 3k – 1) (4k2 – 3k –
1)
= (4k - 1) (k + 1) (4k + 1) (k –
1)

2. a. √ 9w4 = 3w2
√4 = 2
b. (3w2 – 2)2 = (9w4 – 12w2 +4) – 25w2
= (3w2 – 2)2 – 25w2
= [(3w2 - 2) + 5w] [(3w2 - 2) –
5w]
= (3w2 + 5w – 2) (3w2 – 5w – 2)
= (3w - 1) (w + 2) (3w + 1) (w –
2)

3. a. √ 64a4= 8a2
√ b4 = b2
b. (8a2 + b2)2
= (64a4 + 16a2b2 + b4) – 16a2b2
= (8a2 + b2)2 – 16a2b2
= [(8a2 + b2) + 4ab] [(8a2 + b2) –
4ab]
= (8a2 + 4ab + b2) (8a2 – 4ab +
 b2

4. a. √ 49v4 = 7v2

√ (z – 1)2 = (z – 1)

b. [7v2 – (z – 1)]2

= (7v2 + (z – 1)) (7v2 - (z – 1)

= (7v2 + v – 1) (7v2 - z + 1)

IV. ASSIGNMENT

A. Directions: Find the factors of the given polynomial. Show your complete
solution.

1. 100k4 -120k2 + 36
2. 49y4 – 50y2 + 1
3. 4v4 + b4
4. x4 – 4x2 + 16
5. 16h4 + r4

B. Directions: Read and study about Factoring the Sum or Difference of the Same
Odd (Even) Powers.

Demonstrator:
DARLENE A. NATAL

Cooperating Teacher:

MYLA ORDOŇA