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
Multiplying Polynomials
4:40 minutes
Problem 54
Textbook Question
Textbook QuestionFind each product. See Examples 5 and 6. [(9r-s)+2][(9r-s)-2]
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Factoring Difference of Squares
The expression given is in the form of a difference of squares, which follows the identity a^2 - b^2 = (a - b)(a + b). In this case, (9r - s) is treated as 'a' and 2 as 'b'. Recognizing this pattern allows us to simplify the expression efficiently.
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Distributive Property
The distributive property states that a(b + c) = ab + ac. This property is essential for expanding expressions and is used when multiplying the two binomials in the problem. Understanding how to apply this property is crucial for correctly finding the product of the given expression.
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Multiply Polynomials Using the Distributive Property
Combining Like Terms
After expanding the expression, combining like terms is necessary to simplify the result. Like terms are terms that have the same variable raised to the same power. This step ensures that the final expression is in its simplest form, making it easier to interpret and use in further calculations.
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