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Chapter 1: Problem 41

Combine like terms. $$ 9 m n-m n $$

Short Answer

Expert verified
8mn

Step by step solution

01

Identify like terms

Look at each term in the expression to determine which terms can be combined. In this case, both terms, 9mn and -mn, have the same variables (m and n), making them like terms.
02

Combine the coefficients

Add the coefficients of the like terms together. The coefficient of the first term is 9, and the coefficient of the second term is -1 (since -mn is the same as -1mn). So, combine 9 and -1.
03

Simplify

Add the coefficients: 9 + (-1) = 8. This gives us 8mn as the simplified expression.

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Key Concepts

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

Like Terms
When working with algebraic expressions, it's essential to identify 'like terms'. Like terms are terms that contain the exact same variables, raised to the same power. In our expression, 9mn and -mn are like terms because they both contain the variables m and n. The presence of the same variables allows us to combine these terms. If the terms had different variables or different powers, they wouldn't be considered like terms. Understanding this concept is crucial because it simplifies the process of combining terms and reduces the complexity of the expression.
Coefficients
Coefficients are numbers that multiply the variables in an algebraic term. Identifying coefficients is a key step in combining like terms. For example, in the term 9mn, the coefficient is 9. In the term -mn, the coefficient is -1 (since -mn is equivalent to -1mn). Knowing how to identify and work with coefficients allows us to perform operations like addition and subtraction on these terms. When you combine like terms, you essentially add or subtract their coefficients while keeping the variables constant. This step-by-step approach helps in maintaining accuracy and achieving the correct simplified expression.
Simplifying Expressions
Simplifying algebraic expressions by combining like terms is a fundamental skill in algebra. The goal is to make the expression as simple as possible while preserving its mathematical integrity. In our example, the expression 9mn - mn is simplified as follows:
  • Identify like terms: Both 9mn and -mn are like terms because they contain the same variables (m and n).
  • Combine the coefficients: Add the coefficients of these terms. The coefficients are 9 and -1.
  • Perform the arithmetic: 9 + (-1) = 8.
  • Simplify the expression: This results in the simplified expression 8mn.

By understanding and applying these steps, you can simplify any algebraic expression with confidence and ease. Remember, practice makes perfect! The more you work with expressions and terms, the more intuitive this process will become.

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