The document outlines objectives for an eighth-grade mathematics lesson focused on identifying and factoring perfect square trinomials. It provides various examples of expressions to determine if they are perfect square trinomials and includes guidance on factoring them completely. Additionally, it demonstrates the structure of perfect square trinomials with specific formulas and examples.

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