This document provides examples for factoring the sum and difference of two cubes. It defines the factored form of the sum as (x + y)(x^2 - xy + y^2) and the difference as (x - y)(x^2 + xy + y^2). Several examples are worked out step-by-step, rewriting expressions as the sum or difference of two cubes and then factoring into the proper form. The objectives are to identify perfect cubes and factor the sum and difference of two cubes completely.
This will help you in factoring sum and difference of two cubes.
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This presentation explains Algebra in Mathematics. It includes: Introduction, Solution to Puzzle, Definition of terms, Rules in Algebra, Collecting Like Terms, Similar Terms, Expanding the Brackets, Nested Brackets, Multiplication of Algebraic Expressions of a Single Variable, Division of One Expression by another, Addition and Subtraction of Algebraic Fractions, Multiplication and Division of Algebraic Fractions, Factorisation of Algebraic Expression, Useful Products of Two Simple Factors, Examples, Trinomial Expression, Quadratic Expression as the Product of Two Simple Factors, Factorisation of Quadratic Expression ax2 + bx +c When a = 1, Factorisation of Quadratic Expression ax2 + bx +c When a ≠ 1 and Test for Simple Factors.
This will help you in factoring sum and difference of two cubes.
For more instructional resources, CLICK me here!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
This presentation explains Algebra in Mathematics. It includes: Introduction, Solution to Puzzle, Definition of terms, Rules in Algebra, Collecting Like Terms, Similar Terms, Expanding the Brackets, Nested Brackets, Multiplication of Algebraic Expressions of a Single Variable, Division of One Expression by another, Addition and Subtraction of Algebraic Fractions, Multiplication and Division of Algebraic Fractions, Factorisation of Algebraic Expression, Useful Products of Two Simple Factors, Examples, Trinomial Expression, Quadratic Expression as the Product of Two Simple Factors, Factorisation of Quadratic Expression ax2 + bx +c When a = 1, Factorisation of Quadratic Expression ax2 + bx +c When a ≠ 1 and Test for Simple Factors.
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This learner's module discusses or talks about the topic of Quadratic Functions. It also discusses what is Quadratic Functions. It also shows how to transform or rewrite the equation f(x)=ax2 + bx + c to f(x)= a(x-h)2 + k. It will also show the different characteristics of Quadratic Functions.
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APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems.
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difference of two cubes.pdf
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
5. Sum of Two Cubes
𝒙𝟑
+𝒚𝟑
= (x + y)(𝒙𝟐
- xy + 𝒚𝟐
)
x = first term
F
y = last term
L F L 𝑳𝟐
𝑭𝟐
F·L
(x + y)(𝒙𝟐
- xy + 𝒚𝟐
)
FACTORED FORM
6. Factoring Sum of Two Cubes
𝒂𝟑
+ 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)(𝒙𝟐
- xy + 𝒚𝟐
)
( + )( 𝟐
- · + 𝟐
)
x y
a 4 a 4
a 4
7. Factoring Sum of Two Cubes
𝟖𝒃𝟑
+ 𝟐𝟕𝒄𝟑
= ( )𝟑
+ ( )𝟑
Given:
Rewrite as sum of two
cubes:
2b 3c
Supply the missing
terms:
Factored Form (2b + 3c)(4𝑏2
- 6bc + 9𝑐2
)
(x + y)(𝒙𝟐
- xy + 𝒚𝟐
)
( + )[ 𝟐
- · + 𝟐
]
x y
2b 3c (2b) (3c)
2b 3c
8. Difference of Two Cubes
𝒙𝟑
− 𝒚𝟑
= (x - y)(𝒙𝟐
+ xy + 𝒚𝟐
)
x = first term
F
y = last term
L F L 𝑳𝟐
𝑭𝟐
F·L
(x - y)(𝒙𝟐
+ xy + 𝒚𝟐
)
FACTORED FORM
9. Factoring Difference of Two Cubes
𝟐𝟕𝒄𝟑
- 𝒅𝟑
= ( )𝟑
- ( )𝟑
Given:
Rewrite as difference of
two cubes:
3c d
Supply the missing
terms:
Factored Form (3c - d)(9𝑐2
+ 3cd + 𝑑2
)
(x - y)(𝒙𝟐
+ xy + 𝒚𝟐
)
( - )[ 𝟐
+ · + 𝟐
]
x y
3c d (3c) d
(3c) d
10. Factoring Difference of Two Cubes
𝟖𝒆𝟑
𝒇𝟔
- 𝟏𝟐𝟓𝒈𝟑
= ( )𝟑
- ( )𝟑
Given:
Rewrite as difference of
two cubes:
2e𝒇𝟐 5g
Supply the missing
terms:
Factored Form
(2e𝑓2
- 5g)(4e2
𝑓4
+ 10e𝑓2
g + 25𝑔2
)
(x - y)(𝒙𝟐
+ xy + 𝒚𝟐
)
( - )[ 𝟐
+ · + 𝟐
]
x y
2e𝒇𝟐
5g (2e𝒇𝟐
) (5g)
(2e𝒇𝟐
) 5g
11. Factoring Difference of Two Cubes
64 - 𝒑𝟔
= ( )𝟑
- ( )𝟑
Given:
Rewrite as difference of
two cubes:
4 𝒑𝟐
Supply the missing
terms:
Factored Form
(2+p)(2-p)(16 + 4𝑝2
+ 𝑝4
)
(x - y)(𝒙𝟐
+ xy + 𝒚𝟐
)
( - )[ 𝟐
+ · + 𝟐
]
x y
4 𝒑𝟐
4 (𝒑𝟐
)
4 𝒑𝟐
