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Chapter 1: Problem 84

Explain why \(9 a\) and \(3 b\) are not like terms.

Short Answer

Expert verified
The terms \(9a\) and \(3b\) are not like terms because their variables are different.

Step by step solution

01

Identify Coefficients and Variables

Examine the terms separately. For the term \(9a\), identify the coefficient as 9 and the variable as 'a'. For the term \(3b\), identify the coefficient as 3 and the variable as 'b'.
02

Compare the Variables

Determine if the variables in the terms are the same. The term \(9a\) has the variable 'a' and the term \(3b\) has the variable 'b'.
03

Conclusion

Since the variables 'a' and 'b' are different, the terms \(9a\) and \(3b\) are not like terms. Like terms must have the same variable(s) with the same exponent(s).

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Key Concepts

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

coefficients
In algebra, it's vital to understand what a coefficient is. Think of a coefficient as the number in front of the variable in an algebraic expression. In the term \(9a\), the number 9 is the coefficient. It tells you how many times to multiply the variable 'a'.

The term \(3b\) works the same way. Here, 3 is the coefficient, indicating 'b' should be taken three times.

Coefficients are always numerical and can be positive or negative. Recognizing them is the first step in working with algebraic expressions.
  • Coefficients help to scale the variables.
  • A coefficient can be a whole number, fraction, or decimal.
  • It is the 'multiplier' of the variable.
variables
Variables are symbols used to represent numbers in algebra. They are often letters like x, y, or z. In our exercise, the variables are 'a' and 'b'.

Variables can stand for different values and are essential in forming algebraic expressions. They allow us to create rules or formulas that can be applied to many situations.

In the terms \(9a\) and \(3b\), 'a' and 'b' are the variables. Each represents an unknown value that can change.
  • Variables are placeholders for unknown numbers.
  • They are usually written as letters.
  • Variables allow for generalization in math problems.
algebraic expressions
An algebraic expression is a combination of numbers, variables, and operations like addition or multiplication. Examples include \(9a\) and \(3b\).

These expressions are like phrases in math. They convey relationships between numbers and variables.

In algebra, simplifying expressions by combining like terms is common. Like terms have the same variables raised to the same power. For instance, \(2x\) and \(3x\) are like terms because they share the same variable 'x'. But \(9a\) and \(3b\) are not, as they have different variables.
  • Algebraic expressions are made up of terms.
  • Terms can include variables, coefficients, and constants.
  • Expressions can be simplified by combining like terms.

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