This document contains information and examples about perfect square trinomials in algebra. It defines a perfect square trinomial as having a first term and last term that are perfect squares, with a middle term that is twice the product of the square roots of the first and last terms. Examples are provided to illustrate how to identify if an expression is a perfect square trinomial or not. Several activity cards are included that provide practice identifying, factoring, and giving the factors of perfect square trinomial expressions.

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

2. GUIDE CARD
Least Mastered Skill:
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

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 Perfect Square
Trinomial or 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 – 24x + 36
6x2 – 9x + 84
81x2 - 126x + 49
9x2 + 24x + 14
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/3rd
Term

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 - 24x + 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)
a. (x+3)(x+3)
b. (x+3)(x+2)
c. (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