Factoring Sum and Difference of Two Cubes
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The document outlines objectives and methods for factoring the sum and difference of two cubes, providing examples and exercises for middle school students. It includes identifying perfect cubes, factoring expressions like a^3 + b^3 and a^3 - b^3, and filling in missing terms for different algebraic expressions. The material is structured to help students practice and understand these mathematical concepts.
![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](https://image.slidesharecdn.com/edited-200712105751/85/Factoring-Sum-and-Difference-of-Two-Cubes-7-320.jpg)
![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](https://image.slidesharecdn.com/edited-200712105751/85/Factoring-Sum-and-Difference-of-Two-Cubes-9-320.jpg)
![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](https://image.slidesharecdn.com/edited-200712105751/85/Factoring-Sum-and-Difference-of-Two-Cubes-10-320.jpg)
![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](https://image.slidesharecdn.com/edited-200712105751/85/Factoring-Sum-and-Difference-of-Two-Cubes-11-320.jpg)
Factoring Sum and Difference of Two Cubes
- 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