Multiplying a monomial by a binomial

8.4.1 Multiplying a monomial by a binomial

Description

Quick Overview

This section covers how to multiply a monomial by a binomial using the distributive law.

Standard

It provides a method for multiplying monomials and binomials, particularly through the distributive property, ensuring students grasp the structured approach of multiplying each term in the binomial by the monomial and combining like terms.

Detailed

Multiplying a Monomial by a Binomial

In this section, we explore the multiplication of a monomial by a binomial, emphasizing the use of the distributive law to facilitate the process. A monomial is defined as an expression containing only one term, while a binomial is an expression that contains two terms. The distributive property allows us to expand expressions effectively.

To multiply a monomial, such as 3x, by a binomial, like 5y + 2, we use the formula:

3x × (5y + 2) = (3x × 5y) + (3x × 2).

Following the multiplication, we combine the results: 15xy + 6x. The section further illustrates that the order of multiplication does not affect the outcome, as shown by the example that reverses the positions of the monomial and binomial. This foundational concept is critical for understanding more complex polynomial operations later in algebra.

Key Concepts

  • Distributive Law: Necessary rule for multiplying monomials with polynomials.

  • Term Multiplication: Each term in the binomial or polynomial must be multiplied by the monomial.

Memory Aids

🎵 Rhymes Time

  • To multiply a mono and a bino,/ Just distribute as you go,/ Don’t forget to combine the like,/ Or your answer may take a hike.

📖 Fascinating Stories

  • Once there was a clever little monomial named 3x who had a special friendship with the binomial 5y + 2. They loved to party, so every time they met, they multiplied their terms and had fun!

🧠 Other Memory Gems

  • Daisy Eats Sweet Bananas - for 'Distribute Each term in the Sum of the Binomial'.

🎯 Super Acronyms

MATH - Monomial and a Binomial Together Harmoniously.

Examples

  • Example 1: Multiply 3x by the binomial 5y + 2 to get 15xy + 6x.

  • Example 2: Multiply -2a by 3b - 4 to receive -6ab + 8a.

Glossary of Terms

  • Term: Monomial

    Definition:

    An algebraic expression consisting of a single term, such as 3x.

  • Term: Binomial

    Definition:

    An algebraic expression containing two terms, such as 5y + 2.

  • Term: Distributive Law

    Definition:

    A property that states a(b + c) = ab + ac, used for distributing multiplication over addition.

  • Term: Coefficient

    Definition:

    A numerical factor in a term, such as 3 in 3x.