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Chapter 2: Problem 357

In the following exercises, identify the like terms. $$ 5 x^{2}, 3,5 y^{2}, 3 x, x, 4 $$

Short Answer

Expert verified
The like terms are: 5x^2, 5y^2, 3x, x, 3, 4

Step by step solution

01

Identify Terms with the Same Variable and Exponent

Look at each term and determine which ones have the same variable and the same exponent. Terms that have the same variable and exponent are considered like terms.
02

Group the Terms

Group the terms that are identified as like terms in Step 1.
03

List the Like Terms

List each set of like terms that are found in the expression.

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Key Concepts

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

Algebra
Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols. These symbols, commonly letters, represent numbers in equations and formulae. In our exercise, you need to identify like terms, which is a key skill in algebra.
Like terms have identical variables and exponents, which allows for their simplification by combining them. Understanding how to manipulate these terms lets students solve more complex algebraic expressions effectively.
Remember that terms without variables, called constants, are also like terms amongst themselves.
Variable
A variable is a symbol used to represent an unknown value in mathematical expressions and equations. In our exercise, the variables are represented by letters such as 'x' and 'y'.
Variables help us generalize mathematical problems and solutions, allowing us to create formulas that work for different values.
For example, in the terms from the exercise: \(5x^2\), \(3x\), and \(x\), 'x' is the variable that can represent any number.
Recognizing the variables in each term and identifying which terms share the same variable is crucial in simplifying and solving algebraic expressions.
Exponent
An exponent refers to the number that indicates how many times a variable is multiplied by itself. In the term \(5 x^{2}\), the '2' is the exponent. This tells us that 'x' is multiplied by itself once, resulting in \(x \times x\).
Identifying the exponent is essential when working with like terms. Terms must have the same variable and the same exponent to be combined. For instance, \(5x^2\) and \(x\) are not like terms because their exponents differ.
In the given exercise, all terms with the exponent of 鈥�2鈥� for variable 鈥榵鈥�, such as \(5x^2\), are like terms, while terms with different exponents, or with no exponents for the same variable, are not.

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Most popular questions from this chapter

Grocery shopping Paper plates are sold in packages of 12 and party cups come in packs of \(8 .\) What is the smallest number of plates and cups you can purchase if you want to have the same number of each? (Hint: it is the LCM!)

In the following exercises, identify the coefficient of each term. $$ 6 y $$

In the following exercises, find the prime factorization of each number using the factor tree method. $$ 455 $$

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In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5, 6, and 10. $$ 900 $$
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