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Chapter 5: Problem 108

Explain how to multiply monomials. Give an example.

Short Answer

Expert verified
To multiply monomials, multiply the coefficients (numerical parts) together, and then multiply the variables (letters). If the variables are the same, add the exponents. If the variables are different, simply write them next to each other. For example, \(3x\) multiplied by \(4y\) equals \(12xy\).

Step by step solution

01

Introduction

In mathematics, a monomial is an algebraic expression which consists of one term. Terms are separated by '+' or '-' operators, so a monomial will not have these, but can be positive or negative. Examples of monomials are: \(3x\), \(-4y^2\), \(7x^3y^2\), \(2a^3b^4c^5\). The process of multiplying monomials involves the multiplication of coefficients (numerical factors) and multiplication of variables (letter factors).
02

Multiply the coefficients

Multiply the numerical coefficients of the monomials. For example, if you鈥檙e asked to multiply \(3x\) and \(4y\), you should multiply 3 and 4 to get 12.
03

Multiply the variables

If the variables are same, then you keep the base and add the exponents. If the variables are different, just write them side by side. For \(3x\) and \(4y\), the variables are different, so just write them as \(xy\).
04

Write the final result

Bring together the products of the coefficients and variables to represent your final answer. So, for \(3x\) and \(4y\), the answer should be \(12xy\).

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