Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
0. Review of Algebra
Factoring Polynomials
6:05 minutes
Problem 77a
Textbook Question
Textbook QuestionIn Exercises 69–80, factor completely. x³ − y³ − x + y
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Factoring Polynomials
Factoring polynomials involves rewriting a polynomial expression as a product of simpler polynomials. This process is essential for simplifying expressions and solving equations. In the case of the expression x³ − y³ − x + y, recognizing patterns such as the difference of cubes and grouping can aid in the factoring process.
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Difference of Cubes
The difference of cubes is a specific factoring pattern that applies to expressions of the form a³ - b³, which can be factored as (a - b)(a² + ab + b²). In the given expression, x³ - y³ can be identified as a difference of cubes, allowing us to apply this formula to simplify the expression further.
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Grouping Method
The grouping method is a technique used to factor polynomials by rearranging and grouping terms. This method is particularly useful when dealing with four-term polynomials, as it allows for the identification of common factors within groups. In the expression x³ − y³ − x + y, grouping the terms strategically can lead to a complete factorization.
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