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Chapter 10: Problem 18

In the following exercises, add or subtract the monomials. $$-3 m+9 m$$

Short Answer

Expert verified
6m

Step by step solution

01

Identify the Like Terms

Check if the terms are like terms. Like terms have the same variable raised to the same power. Here, both terms (-3m) and (9m) have the same variable 'm'.
02

Add or Subtract the Coefficients

Since the terms are like terms, subtract the coefficients (-3 and 9). The variable 'm' does not change. Hence: -3 + 9 = 6
03

Combine the Terms

Write down the result from Step 2 with the common variable 'm'. The final expression is: 6m

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Key Concepts

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

Monomials
In algebra, a monomial is a mathematical expression that consists of a single term. This term can be a constant, a variable, or a product of constants and variables. For example, 5, -3x, and 7y虏 are all monomials.
Monomials do not contain any addition or subtraction signs within them. This simplicity helps in combining like terms.
When dealing with monomials, it is crucial to identify their components, such as the coefficient and the variable part.
Remember, monomials with the same variables raised to the same power are considered like terms.
Coefficients
A coefficient is the numerical part of a term that appears in front of the variable. For instance, in the term 9m, 9 is the coefficient.
The role of the coefficient is to multiply the variable part of the term. When combining like terms, we add or subtract the coefficients while keeping the variable part unchanged.
For example, in the expression -3m + 9m, we combine like terms by subtracting the coefficients: -3 + 9 = 6. Therefore, the combined term is 6m.
Always ensure that coefficients are correctly combined to simplify algebraic expressions accurately.
Prealgebra
Prealgebra is the foundational course that introduces basic algebraic concepts to students. Combining like terms, such as monomials, is one of these core concepts.
Understanding prealgebra lays the groundwork for more advanced mathematical concepts. For example, recognizing like terms and coefficients helps in simplifying expressions and solving equations.
When studying prealgebra, practice problems like adding and subtracting monomials are essential. This skill helps in developing a solid understanding of algebraic operations.
Remember, regular practice and familiarity with the terminology will make the transition to algebra smoother and more intuitive.

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