Problem 145 In the following exercises, iden... [FREE SOLUTION]

Chapter 1: Problem 145

In the following exercises, identify the like terms. $$ x^{3}, 8 x, 14,8 y, 5,8 x^{3} $$

Short Answer

Expert verified

The like terms are: $x^{3}, 8x^{3}$, $8x$, $14, 5$, $8y$.

Step by step solution

- Identify terms involving the same variables raised to the same power

Check each term and note the variables and their exponents. Identify terms that have the same variable and the same exponent.

- Group the like terms

Combine the terms that match based on the variables and their exponents.

- Provide the final groups of like terms

List the groups of like terms based on the previous step.

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Key Concepts

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

Variables

Variables are symbols used to represent unknown values in mathematical expressions. Common variables include letters like x, y, and z. In algebra, variables can change depending on the equation or context. In the exercise, we see variables are used in three terms: $x^3$, $8x$, and $8y$. Each term involves a variable that may be raised to different powers.
Here are key points about variables:

Variables are essential in representing equations and expressions.
They can be any letter or symbol, but commonly, letters from the alphabet are used.

Exponents

Exponents refer to the power to which a number or variable is raised. They tell us how many times to use the base variable in a multiplication. For example, in the term $x^3$, the exponent is 3, indicating that x is multiplied by itself three times: $x \times x \times x$.
In the exercise, understanding the exponents is crucial for identifying like terms:

$x^3$ and $8x^3$ have the same variable 'x' raised to the same power.
$8x$ and $8y$ have different exponents and variables, so they are different.

Exponents are what make identifying like terms straightforward. Terms need to have the same variable with the same exponent to be considered like.

Grouping Terms

Grouping terms is an important step in simplifying algebraic expressions. To group terms correctly:

First, identify terms that have the same variable raised to the same power. These are 'like terms'.
Combine or list these like terms to simplify the expression.

In the exercise, we identify the like terms:

$x^3$ and $8x^3$ have the same variable and power.
The constant terms, 14 and 5, are also like terms because they don鈥檛 have variables.

Thus, the final groups of like terms are: $[x^3, 8x^3], [8x], [8y], [14, 5]$. Grouping terms helps in simplifying and solving complex expressions efficiently.

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91影视

In the following exercises, identify the like terms. $$ x^{3}, 8 x, 14,8 y, 5,8 x^{3} $$

Short Answer

Step by step solution

- Identify terms involving the same variables raised to the same power

- Group the like terms

- Provide the final groups of like terms

Key Concepts

Variables

Exponents

Grouping Terms

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