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Chapter 1: Problem 42

Combine like terms. $$ 3 c m-c m $$

Short Answer

Expert verified
2 cm

Step by step solution

01

Identify like terms

First, recognize that the terms in the expression are like terms because they both contain the variable \(cm\).
02

Combine coefficients

Combine the coefficients of the like terms. Here, the coefficients are 3 and -1 (since \(- cm\) is the same as \(-1 \cdot cm\)). Thus, we have: \[ 3 - 1 \]
03

Simplify the expression

Subtract 1 from 3: \[ 3 - 1 = 2 \] This means we have \[ 2 cm \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

like terms
In algebra, different terms are considered 'like terms' if they have identical variable parts. For example, in the expression from the exercise, both terms have the same variable combination:
cm. This means they can be combined. Identifying like terms is crucial because it tells us which terms we can add or subtract together.
Like terms simplify expressions and make calculations easier. They often appear in equations with multiple terms, and by combining them, you reduce the complexity of the problem.
coefficients
Coefficients are the numerical parts of terms that are to be multiplied by the variables. In the problem, the terms are [3 cm] and [- cm]. Here, [3] is the coefficient of [cm], and since the second term is [- cm], it implies the coefficient is [-1].
Understanding coefficients is important when combining like terms because you need to look at their multiplication values and operations between them. For instance, if you have 3 cm and -1 cm, you combine their coefficients: [3 + (-1) = 2]. This simplified term makes your expression easier to handle and solve.
simplify expressions
Simplifying expressions is the process of making an expression shorter and easier to understand by combining like terms. In the exercise, you started with [3 cm - cm]. By combining the like terms, you combined their coefficients.
First, you identified that both terms had the variable [cm]. Then, you noted their coefficients were 3 and -1. Finally, you combined the coefficients by subtraction: [3 - 1 = 2]. Therefore, the simplified expression is [2 cm].
Simplifying helps in solving equations faster and understanding the relationships between different terms more clearly. Always look for like terms in your expressions and combine their coefficients to make your work simpler.

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