Multiplying three or more monomials

8.3.2 Multiplying three or more monomials

Description

Quick Overview

This section explains how to multiply three or more monomials together, illustrating the process with various examples.

Standard

In this section, students learn the systematic approach to multiplying three or more monomials, including the importance of grouping and combining like terms. The section provides detailed examples to solidify understanding, reinforcing the concepts of coefficients, variables, and powers.

Detailed

Multiplying Three or More Monomials

In this section, we extend our understanding of multiplication from two monomials to three or more. The multiplication of monomials involves multiplying their coefficients and adding the exponents of like bases. This section highlights the associative property of multiplication, allowing us to group terms in any order for ease of calculation.

For example, when multiplying the monomials 2x, 5y, and 7z, we first pair and multiply:

  1. Multiply the first two: (2x × 5y) = 10xy.
  2. Then multiply the result by the third: 10xy × 7z = 70xyz.

The section also discusses multiplying monomials with like bases, ensuring that students know to add the exponents when the bases are the same. Another example is multiplying 4xy × 5x²y² × 6x³y³. Here, we multiply the coefficients first: 4 × 5 × 6 = 120, and then the variables, combining like bases to yield: 120x^(1+2+3)y^(1+2+3) = 120x^6y^6.

This detailed exposition not only teaches the mechanics of multiplication but emphasizes their practical applications in geometry and volume calculations as well.

Key Concepts

  • Multiplication of Monomials: The process of multiplying monomial coefficients and adding the exponents of like bases.

  • Associative Property: The order in which you multiply monomials does not matter.

  • Combining Like Terms: During multiplication, like variables should have their exponents added.

Memory Aids

🎵 Rhymes Time

  • When you multiply monomials, be wise, coefficients multiplied and exponents added, that's the prize!

📖 Fascinating Stories

  • Imagine a garden where each flower grows taller each year; the height doubles and your job is to mix flowers. As you mix, remember to add the height from previous years, this is how we multiply and grow in understanding!

🧠 Other Memory Gems

  • MICE: Multiply coefficients, Identify like terms, Combine exponents, and Evaluate the result.

🎯 Super Acronyms

M2E

  • Multiply
  • then Merge exponents!

Examples

  • Example of three monomials: 2x, 5y, and 7z gives 70xyz.

  • Example of complex monomials: 4xy × 5x^2y^2 × 6x^3y^3 results in 120x^6y^6.

Glossary of Terms

  • Term: Monomial

    Definition:

    An algebraic expression that consists of a single term.

  • Term: Coefficient

    Definition:

    The numerical factor in a term of an expression.

  • Term: Exponent

    Definition:

    The power to which a number or expression is raised.

  • Term: Like Bases

    Definition:

    Variables that are the same and whose exponents can be added.