Republic of the Philippines
Department of Education
REGION XII
DIVISION OF GENERAL SANTOS CITY
Mathematics 8
“Factoring Perfect Square
Trinomials”
Quarter 1, Week 1 Day 4
OBJECTIVES
• Recognize if a given trinomial is a perfect
square.
• Factor completely a perfect square
trinomial.
• Participate actively in class activities.
ACTIVITY 1: Cross It Out!
Direction: Given the table, cross out all perfect squares.
10 6 111 81
55 13 36 0
70 144 23 22
4 22 41 125
24 64 88 80
21 77 9 54
90 60 3 100
222
16
19
37
50
49
5
8
17
25
99
121
44
45
11
33
90
1
68
12
66
Guide questions:
1. Were you able to find all perfect squares?
2. How did you know that these numbers are perfect squares?
ACTIVITY 2: Go, and Multiply!
Direction: Square the following binomials in Column A and match
its product in Column B.
Guide questions:
1. State the steps in squaring a binomial.
2. How many resulting terms when we square binomial?
ACTIVITY 3: Compare Us!
Direction: Compare and contrast the problems below.
Guide questions:
1. Did you observe any pattern?
2. Is there a relationship between squaring a binomial and
factoring perfect square trinomial?
LESSON PROPER
A Perfect square trinomial is the result of squaring a
binomial, wherein there are characteristics that would
help us determine if the given trinomial is perfect or
not.
∙ The first and last terms must be both positive
and must be perfect squares.
∙ The middle term is twice the product of the
square root of the first and last terms.
EXAMPLES
Perfect Square Trinomials (PST)
1. x2 – 2x + 1
2. x2 + 14x + 49
3. x2 – 18x + 81
4. 4x2 + 20x + 25
5. 9x2 + 12xy + 4y2
FACTORING PERFECT SQUARE TRINOMIALS
To factor perfect square trinomials:
1. Verify if the given polynomial is a perfect
square trinomial.
2. Get the square root of the first and last terms.
3. Express them as a square of a binomial following
the sign of the middle term.
***Remember to factor out first the greatest common monomial
factor before factoring the perfect square trinomial.
Examples: Factor the following.
x2 – 16x + 64
Solution:
a. Check if the given polynomial is a PST.
x2 – 16x + 64 = (x)2 – 2(8x) + (8)2
It is a PST, since the first and last term are
both positive and the middle term is twice the
product of the first and last term.
b. Since the sign of the middle term is negative,
we will express the PST as the square of the
difference of x and 8.
x2 – 16x + 64 = (x – 8)(x – 8) = (x – 8)2
ACTIVITY 4: Thumbs Up or Down!
Direction: In each statement, identify whether it is TRUE or
FALSE. If it is true, raise thumbs up and otherwise thumbs down.
1. Factoring perfect square trinomials is simply the
reverse of squaring a binomial.
2. The first and last terms of a perfect square trinomial
should be perfect squares and positive.
3. The middle term of a perfect square trinomial is
sometimes twice the product of the square root of
the first and last terms.
4. x2 – 15x + 36 is a perfect square trinomial.
5. 4x2 + 12x + 9 is a perfect square trinomial.
ACTIVITY 4: Thumbs Up or Down!
Direction: In each statement, identify whether it is true or false. If
it is true, raise thumbs up and otherwise thumbs down.
6. x2 + 18x + 81 is not a perfect square trinomial.
7. The factors of x2 + 14x + 49 are (x + 7)(x + 7).
8. The factors of 9x2 – 30x + 25 are (3x + 5)(3x + 5).
9. 4x2 + 12xy + 36y2 = (2x + 6)2
10. 2x2 + 12x + 18 = 2(x + 3)2
SUMMARY
When is a trinomial a perfect square?
-When the first and last terms are perfect
squares, and both are positive.
-When the middle term is twice the product of
the square root of the first and last terms.
SUMMARY
How do you know when the factors of a perfect
square trinomial is a square of a sum or difference
of two terms?
*(x + y)2 , if the middle sign is positive.
*(x – y)2 , if the middle sign is negative.
INDIVIDUAL QUIZ
A. Direction: Write PST if the given is a perfect square trinomial,
otherwise write NPST.
INDIVIDUAL QUIZ
B. Direction: Factoring the following perfect square trinomials
completely.
ACTIVITY 5: Lead Me The Way!
Direction: Move through the maze from start to finish by factoring
each perfect square trinomial completely.
Republic of the Philippines
Department of Education
REGION XII
DIVISION OF GENERAL SANTOS CITY
THANK YOU!
Basta galing Gensan, galíng
Gensan!
Dahil una sa lahat, Bata!!!
ACTIVITY 5: Lead Me The Way!
DEVELOPMENT TEAM
Writer:
Leslie A. Aban
Content Editor: Zaida N. Abiera
LR Evaluator:
Mary Jane V. Muyco
Management Team:
Isagani S. Dela Cruz, CESO V – Schools Division Superintendent
Carlos G. Susarno, CESE – Asst. Schools Division Superintendent
Juliet F. Lastimosa – CID Chief
Aileen A. Jamero - Division EPS, LRMS
Zaida N. Abiera – Division EPS, Mathematics