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1. Grade 8 – Mathematics
Quarter I
FACTORING: SUM AND
DIFFERENCE OF TWO CUBES

2. Objectives:
1. identify whether or not an
expression is a perfect cube; and
2. factor the sum and difference of
two cubes completely;

3. Tell whether the following number
is a perfect cube or not.
1. 8
2. 25
3. 64
4. 40
5. 27
6. 60
7. 125
8. 72
9. 216
10.343
PERFECT CUBE
NOT
PERFECT CUBE
PERFECT CUBE
PERFECT CUBE
NOT
PERFECT CUBE
NOT
NOT
PERFECT CUBE

4. 1. 23
2. 33
3. 43
4. 53
5. 63
6. 73
2x2x2 = 8
3x3x3 = 27
4x4x4 = 64
5x5x5 = 125
6x6x6 = 216
7x7x7 = 343
Evaluate each exponential notation.

5. Sum of Two Cubes
𝒙 𝟑
+𝒚 𝟑
= (x + y)(𝒙 𝟐
- xy + 𝒚 𝟐
)
x = first term
F
y = last term
L F L 𝑳 𝟐𝑭 𝟐
F·L
(x + y)(𝒙 𝟐
- xy + 𝒚 𝟐
)
FACTORED FORM

6. Factoring Sum of Two Cubes
𝒂 𝟑
+ 64
= ( ) 𝟑
+ ( ) 𝟑
Given:
Rewrite as sum of two
cubes:
a 4
Supply the missing
terms:
Factored Form (a + 4)(𝑎2
- 4a + 16)
(x + y)(𝒙 𝟐
- xy + 𝒚 𝟐
)
( + )( 𝟐
- · + 𝟐
)
x y
a 4 a 4a 4

7. Factoring Sum of Two Cubes
𝟖𝒃 𝟑
+ 𝟐𝟕𝒄 𝟑
= ( ) 𝟑
+ ( ) 𝟑
Given:
Rewrite as sum of two
cubes:
2b 3c
Supply the missing
terms:
Factored Form (2b + 3c)(4𝑏2
- 6bc + 9𝑐2
)
(x + y)(𝒙 𝟐
- xy + 𝒚 𝟐
)
( + )[ 𝟐
- · + 𝟐
]
x y
2b 3c (2b) (3c)2b 3c

8. Difference of Two Cubes
𝒙 𝟑
− 𝒚 𝟑
= (x - y)(𝒙 𝟐
+ xy + 𝒚 𝟐
)
x = first term
F
y = last term
L F L 𝑳 𝟐𝑭 𝟐
F·L
(x - y)(𝒙 𝟐
+ xy + 𝒚 𝟐
)
FACTORED FORM

9. Factoring Difference of Two Cubes
𝟐𝟕𝒄 𝟑
- 𝒅 𝟑
= ( ) 𝟑
- ( ) 𝟑
Given:
Rewrite as difference of
two cubes:
3c d
Supply the missing
terms:
Factored Form (3c - d)(9𝑐2
+ 3cd + 𝑑2
)
(x - y)(𝒙 𝟐
+ xy + 𝒚 𝟐
)
( - )[ 𝟐
+ · + 𝟐
]
x y
3c d (3c) d(3c) d

10. Factoring Difference of Two Cubes
𝟖𝒆 𝟑
𝒇 𝟔
- 𝟏𝟐𝟓𝒈 𝟑
= ( ) 𝟑
- ( ) 𝟑
Given:
Rewrite as difference of
two cubes:
2e𝒇 𝟐 5g
Supply the missing
terms:
Factored Form
(2e𝑓2
- 5g)(4e2
𝑓4
+ 10e𝑓2
g + 25𝑔2
)
(x - y)(𝒙 𝟐
+ xy + 𝒚 𝟐
)
( - )[ 𝟐
+ · + 𝟐
]
x y
2e𝒇 𝟐
5g (2e𝒇 𝟐
) (5g)(2e𝒇 𝟐
) 5g

11. Factoring Difference of Two Cubes
64 - 𝒑 𝟔
= ( ) 𝟑
- ( ) 𝟑
Given:
Rewrite as difference of
two cubes:
4 𝒑 𝟐
Supply the missing
terms:
Factored Form
(2+p)(2-p)(16 + 4𝑝2
+ 𝑝4
)
(x - y)(𝒙 𝟐
+ xy + 𝒚 𝟐
)
( - )[ 𝟐
+ · + 𝟐
]
x y
4 𝒑 𝟐
4 (𝒑 𝟐
)4 𝒑 𝟐