Problem 357 In the following exercises, iden... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

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

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.

Group the Terms

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

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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91影视

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

Short Answer

Step by step solution

Identify Terms with the Same Variable and Exponent

Group the Terms

List the Like Terms

Key Concepts

Algebra

Variable

Exponent

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