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Multiply the polynomials using special product formulas.
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0. Review of Algebra
Multiplying Polynomials
2:04 minutiProblema 11
Domanda del libro di testo
In Exercises 9–22, multiply the monomial and the polynomial. 2y(y²−5y)
Guida verificata passo dopo passo1
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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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.
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Introduction to Polynomials
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.
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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 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.
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