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Chapter 1: Problem 35

Identify each group of terms as like or unlike. \(8 r,-13 r\)

Short Answer

Expert verified
Like terms.

Step by step solution

01

Identify Variables

Determine if the terms share the same variable component. Both terms are given as: \(8r\) and \(-13r\).
02

Identify Exponents

Check if the exponents of the variables in each term are the same. Here, \(8r\) and \(-13r\) both have the variable \(r\) raised to the power of 1.
03

Conclude Like or Unlike Terms

Since both terms have the same variable \(r\) with the same exponent (1), they are like terms.

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Key Concepts

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

Variables
When you study algebra, you'll often see symbols like x, y, or r. These are called variables. Variables represent unknown numbers in equations and expressions. For example, in the terms 8r and -13r, 'r' is the variable.
Variables can stand for different values. This means they are flexible and can change depending on the problem you are solving. Understanding variables is key to solving many algebra problems. Without variables, it would be very hard to write and solve complex equations.
Exponents
An exponent tells you how many times to multiply a number by itself. For instance, in the expression x^2, the 2 is an exponent. It tells you to multiply x by itself: x * x.
In the terms 8r and -13r, each 'r' has an implied exponent of 1. This means it is just 'r' and not 'r' squared or 'r' cubed. Exponents are important in algebra because they affect how you simplify and compare terms. When identifying like terms, the exponents must be the same. If one term was r^2 and another was r, they would not be like terms.
Algebra
Algebra is a branch of mathematics that uses symbols (like variables) to represent numbers and analyze relationships between them.
Algebra helps you solve equations and understand how variables interact with each other. For instance, you can use algebra to solve for a variable in an equation like 5 + x = 12. By subtracting 5 from both sides, you find that x = 7.
In the exercise given, algebraic understanding helps you identify that 8r and -13r are like terms because they both contain the same variable 鈥榬鈥� with the same exponent. This core concept of algebra makes it easier to solve and simplify many different types of problems.

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Most popular questions from this chapter

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