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
Polynomials Intro
4:02 minutes
Problem 17a
Textbook Question
Textbook QuestionIn Exercises 9–22, multiply the monomial and the polynomial. 3ab² (6a²b³+5ab)
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Monomials
A monomial is a single term algebraic expression that consists of a coefficient and variables raised to non-negative integer powers. For example, in the expression 3ab², 3 is the coefficient, and ab² represents the variables a and b raised to the second power. Understanding monomials is essential for performing operations like multiplication with polynomials.
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Polynomials
A polynomial is an algebraic expression that consists of one or more terms, where each term is a product of a coefficient and variables raised to non-negative integer powers. The expression 6a²b³ + 5ab is a polynomial with two terms. Recognizing the structure of polynomials is crucial for applying algebraic operations such as multiplication.
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Distributive Property
The distributive property states that a(b + c) = ab + ac, allowing us to multiply a single term by each term in a polynomial. In the given problem, applying this property enables the multiplication of the monomial 3ab² with each term of the polynomial, resulting in a simplified expression. Mastery of this property is vital for efficiently solving algebraic expressions.
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