This document provides guidance on identifying and factoring perfect square trinomials in algebra. It begins with a definition of a perfect square trinomial as a trinomial that results from squaring a binomial. Examples are provided to illustrate this. Several activity cards are then presented to help students practice determining if an expression is a perfect square trinomial, completing the terms, factoring, and more. An enrichment card adds an assessment with multiple choice questions. Key steps for factoring a perfect square trinomial are outlined, such as taking the square root of the first and last terms. An answer card provides the solutions to the activities. Sources are listed at the end.

1. In Mathematics VIII
Prepared by:
SHERYL B. DELA CRUZ
Teacher I

2. GUIDE CARD
LeastMasteredSkill:
Sub tasks:
Determine whether the given algebraic expression is
perfect square trinomial or not.
Complete the terms of the expression in the product
of the given factor of perfect square trinomial..
Give the missing factor of the perfect square
trinomial
Determine the Factor of perfect square trinomial.

3. What is
Perfect
Square
Trinomial?
A PERFECT SQUARE
TRINOMIAL is the result
of squaring a binomial.
Example:
(x + y)2 or (x + y) (x + y) = x2 + 2xy + y2
Therefore,
x2 + 2xy + y2 is a PERFECT
SQUARE TRINOMIAL!
Correct!

4. Activity Card 1
Direction : Complete the terms. Write your answer in the space provided.
1. (x-y)(x-y) = x2 – 2xy + _______ 2. (2m+5)(2m+5) = _____ +20m + _____
3. (x+6)2 = x2 + _____ + _______ 4. (3a - 2)2 = _____ - 12a + ______

5. A PERFECT SQUARE TRINOMIAL has FIRST and LAST terms which are PERFECT
SQUARE, and a MIDDLE term is twice the product of the square root of the FIRST and LAST
terms.
Example : x2 + 6x + 9 is Perfect Square Trinomial, because
X2 and 9 are Perfect Square
𝑥2 = X 6x is 2 ( X )( 3 )
9 = 3
How do we easily identify if the given trinomial is a Perfect Square? Or not?
First Term Last Term
MiddleTerm
First Term
Last Term
MiddleTerm

6. Activity Card # 2
Am I PerfectSquare
Trinomialor not?
Direction: Write PST if the given expression is Perfect Square Trinomial and
NOT PST if the given expression is not Perfect Square Trinomial.
x2 + 4x + 41.
4x2 + 5x + 1
x2 – 12x + 36
6x2 – 9x + 84
81x2 - 126x + 49
9x2 + 24x + 16
2.
3.
4.
5.
6.

8. To factor Perfect Square Trinomial:
Example: x2 + 18x + 81
1. Get the square root of the first term and the last term.
𝑥2 = x
81 = 9
2. List down the square root as sum or difference of two
terms as the case may be.
(x+ 9)2 or (x+9) (x+9)
Is there any
pattern in
factoring Perfect
Square
Trinomial?
YES! You may use the following relationship to factor:
(1st term)2 + 2(1st term)(last term) + (last term)2 = (1st + last)2
(1st term)2 - 2(1st term)(last term) + (last term)2 = (1st - last)2
X2 – 14x + 49 = (x – 7)2 or (x-7)(x-7)
X2 72
2 (x) (7) = 14x
First Term 2nd Term
Last/3rdT
erm

9. Activity Card # 3
Direction: Give the missing factor of Perfect Square Trinomial.
1. x2 + 2x + 1 = (_____) (x + 1) 3. 9x4 - 24x + 16y2 = (3x2 – 4y) (____)
4. 16x2 + 24x + 9 = (____) (____)2. 4x2 - 12x + 9 = (2x - 3) (____)

10. ACTIVITY CARD # 4
True
or
False
1. 9x2 + 4x + 1 = (3x+1)2
2. 4x2 - 16x + 16 = (2x-4)2
3. x2 + 14x + 49 = (x+7)2
4. 16x2 - 24xy + 9y2 = (4x-3y)2
Direction: Write TRUE if the corresponding factor is correct and FALSE if it is not.

11. 1. 4x2 – 16x + 16 =
________________
2. x2 + 12x + 36 =
________________
3. x2 – 14x + 49 =
________________
4. 9x2 + 6xy + y2 =
________________
5. x2 – 10x + 25 =
________________
ACTIVITY CARD # 5
Direction : Give the factor of the following Perfect Square Trinomial.

12. Enrichment Card

13. Direction : Encircle the letter of the correct answer.
1. Which of the
following
factors give a
product of
x2 +6x+9?
a. (x+3)(x-3)
b. (x+3)(x+3)
c. (x+3)(x+2)
d. (x+6)(x+3)
2. Which of the
following is perfect
square trinomial?
a. x2 + 3x + 16
b. x2 -18x + 9
c. x2 + 2x +1
d. 25 x2 + 25x +4
3. Which of the
following values of
k will make
x2 +8x + k perfect
square trinomial?
a. -16
b. 16
c. 64
d. -64
4. Which of the following
is Correct?
a. x2 +4x+4 = (x+4)2
b. X2 -12x +36 =(x+2)(x-6)
c. X2 +7x + 49 = (X+ 7)(x-7)
d. X2 -10x+25 =(x-5)2
5. What is the
factor of
64x2 +16x +1?
a. (8x+1)2
b. (8x -1)(8x+1)
c. (8x -1)2
d. (8x-2) (8x+2)
Assessment Card

14. Answer Card
Activity Card
1
1. Y2
2. 4m2 and 25
3. 12x and 36
4. 9a2 and 4
Activity Card
2
1. PST
2. NOT PST
3. PST
4. NOT PST
5. PST
6. PST
Activity Card 3
1. X + 1
2. 2x - 3
3. 3x2 – 4y
4. (4x + 3)(4x + 3)
Activity Card 4
1. FALSE
2. TRUE
3. TRUE
4. TRUE
Activity Card 5
1. (2x – 4)2
2. (x + 6)2
3. (x– 7)2
4. (3x + y)2
5. (x - 5)2
Enrichment
Card
Yes!
The measure of
each sides is
(2x -3)2.
Assessment
Card
1. b
2. c
3. b
4. d
5. a
Lesson
LearnedI learned _________
_________________
_________________
_________________
_________________
_________________
_________________

15. Emmanuel P. Abuzo, Mathematics Learner’ Module. Book Media Press, Inc.
21-E,Boni Serrano Ave., Q.C. First Edition, 2013.
Soledad Jose – Dilao, Ed. D, Intermediate Algebra II. SD Publications, Inc. G.
Araneta Ave.cor. Ma. Clara St. 1107 Q.C. Philippines. Copy right 2009
http://www.basic-mathematics.com/factoring-perfect-square-trinomials.html.