Table of contents

0. Review of Algebra4h 18m
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 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Multiplying Polynomials

College Algebra

0. Review of Algebra

Multiplying Polynomials

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2:04 minutes

Problem 11

Textbook Question

In Exercises 9–22, multiply the monomial and the polynomial.2y(y²−5y)

Verified step by step guidance

Identify the expression to be multiplied: \(2y(y^2 - 5y)\).

Apply the distributive property: multiply \(2y\) by each term inside the parentheses.

First, multiply \(2y\) by \(y^2\): \(2y \cdot y^2\).

Next, multiply \(2y\) by \(-5y\): \(2y \cdot (-5y)\).

Combine the results of the multiplications to form the expanded expression.

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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 polynomial with only one term, which can be a constant, a variable, or a product of constants and variables raised to non-negative integer powers. In the given expression, '2y' is a monomial, representing a single term that can be multiplied with other expressions.

Polynomials

A polynomial is an algebraic expression that consists of one or more terms, where each term includes a variable raised to a non-negative integer exponent and a coefficient. The expression '(y² - 5y)' is a polynomial with two terms, indicating that it can be manipulated through operations like addition, subtraction, and multiplication.

Distributive Property

The distributive property states that a(b + c) = ab + ac, allowing us to multiply a single term by each term within a parenthesis. In this exercise, applying the distributive property will enable us to multiply the monomial '2y' by each term in the polynomial '(y² - 5y)', resulting in a simplified expression.