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Welcome to our Math lesson on Expanding the Algebraic Expression of the Form (a + b) · (a2 - ab + b2), this is the eighth lesson of our suite of math lessons covering the topic of Special Algebraic Identities Obtained through Expanding, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Expanding the Algebraic Expression of the Form (a + b) · (a2 - ab + b2)
As we said earlier, this is a similar expression to the previous one; hence, the approach is also the same. We have
(a + b) ∙ (a2 - ab + b2 )
= a ∙ a2 + a ∙ (-ab) + a ∙ b2 + b ∙ a2 + b ∙ (-ab) + b ∙ b2
= a3 - a2 b + ab2 + a2 b - ab2 + b3
= a3 + b3
Example 7
Simplify the following expression.
(1 + x)(1 - x + x2)
Solution 7
This is an expression of the form (a + b)·(a2 - ab + b2), where a = 1 and b = x.
Giving that, after expanding, this expression shortens too much based on the formula
(a + b) ∙ (a2 - ab + b2 ) = a3 + b3
we don't need to make operations with all terms but simply write
(1 + x)(1 - x + x2 )
= (1 + x)(12 - 1 ∙ x + x2 )
= 13 + x3
= 1 + x3
More Special Algebraic Identities Obtained through Expanding Lessons and Learning Resources
Expressions Learning Material| Tutorial ID | Math Tutorial Title | Tutorial | Video
Tutorial | Revision
Notes | Revision
Questions |
|---|
| 6.3 | Special Algebraic Identities Obtained through Expanding | | | | |
| Lesson ID | Math Lesson Title | Lesson | Video
Lesson |
|---|
| 6.3.1 | The Meaning of a Binomial | | |
| 6.3.2 | Square of a Sum | | |
| 6.3.3 | Square of a Difference | | |
| 6.3.4 | Product of Conjugates | | |
| 6.3.5 | Cube of a Sum | | |
| 6.3.6 | Cube of a Difference | | |
| 6.3.7 | Expanding the Algebraic Expression of the Form (a - b) · (a2 + ab + b2) | | |
| 6.3.8 | Expanding the Algebraic Expression of the Form (a + b) · (a2 - ab + b2) | | |
| 6.3.9 | Expanding Expressions of the Form (a + b + c)2 | | |
| 6.3.10 | Combining Special Identities | | |
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- Algebraic Expression A Plus B Feedback. Helps other - Leave a rating for this algebraic expression a plus b (see below)
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- Continuing learning expressions - read our next math tutorial: Factorising
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