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1. Grade 8 – Mathematics
Quarter I
FACTORING
PERFECT SQUARE TRINOMIALS

2. Objectives:
1. identify whether or not an
expression is a perfect square
trinomial; and
2. factor perfect square trinomials
completely.

3. Tell whether the following expression is
a perfect square trinomial or not.
1. 𝑥2
+ 2xy + 𝑦2
2. 4𝑥2
+ 20x + 25
3. 𝑥2
+ 5x + 6
4. 9𝑥2
+ 30xy + 25𝑦2
5. 4𝑥2
+ 2xy + 𝑦2
PERFECT SQUARE
TRINOMIAL
PERFECT SQUARE
TRINOMIAL
NOT
NOT
PERFECT SQUARE
TRINOMIAL

4. PERFECT SQUARE TRINOMIAL
1. 𝑥2
+ 2xy + 𝑦2
( )2
+ 2( )( ) + ( )2
2. 4𝑥2
+ 20x + 25
( )2
+ 2( )( ) + ( )2
x yx y
2x 52x 5
FIRST TERM
PERFECT
SQUARE
MIDDLE TERM
TWICE THE PRODUCT
of first and last term
LAST TERM
PERFECT
SQUARE
(positive)(positive)

5. PERFECT SQUARE TRINOMIAL
3. 𝑥2
+ 5x + 6
( )2
+ 2( )( ) + ( )2
4. 9𝑥2
+ 30xy + 25𝑦2
( )2
+ 2( )( ) + ( )2
5. 4𝑥2
+ 2xy + 𝑦2
( )2
+ 2( )( ) + ( )2
x ?x ?
3x 5y3x 5y
2x 2x yy
NOT
NOT

6. FACTORING PERFECT SQUARE TRINOMIALS
= ( 𝐱 + 𝒚) 𝟐(𝒙 𝟐
+ 2xy + 𝒚 𝟐
)
FACTORED
FORM
= ( 𝐱 − 𝒚) 𝟐(𝒙 𝟐
- 2xy + 𝒚 𝟐
)
First FirstLast Last

7. FACTOR.
𝑥2
+ 10x + 25 = ( 𝐱 + 𝒚) 𝟐
Check: ( )2
+ 2( )( ) + ( )2
Factored Form: = ( + ) 𝟐
x 5x 5
x 5
16𝑥2
+ 72x + 81 = ( 𝐱 + 𝒚) 𝟐
Check: ( )2
+ 2( )( ) + ( )2
Factored Form: = ( + ) 𝟐
4x 94x 9
4x 9

8. FACTOR.
25𝑚2
− 20mn + 4𝑛2
= ( 𝐱 − 𝒚) 𝟐
Check: ( )2
− 2( )( )+( )2
Factored Form: = ( − ) 𝟐
5m 2n5m 2n
5m 2n
𝑥2
− 22x + 121 = ( 𝐱 − 𝒚) 𝟐
Check: ( )2
− 2( )( ) + ( )2
Factored Form: = ( − ) 𝟐
x 11x 11
x 11

9. FACTOR.
27𝑎2
+ 72ab + 48𝑏2
Factor out 3: 3( + + )
Factored Form: 3( + ) 𝟐
16𝑏2
9𝑎2 24ab
3a 4b
4𝑥3
− 24𝑥2
+ 36x
Factor out 4x: 4x( - + )
Factored Form: 4x( − ) 𝟐
9𝑥2 6x
x 3