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

Verified step by step guidance

1. Identify the expression to be multiplied: \(2y(y^2 - 5y)\).
2. Apply the distributive property: multiply \(2y\) by each term inside the parentheses.
3. First, multiply \(2y\) by \(y^2\): \(2y \cdot y^2\).
4. Next, multiply \(2y\) by \(-5y\): \(2y \cdot (-5y)\).
5. Combine the results of the multiplications to form the expanded expression.

Key Concepts

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.