Problem 17 Determine if the terms are like ... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 10: Problem 17

Determine if the terms are like terms. $$-6 x \quad and\quad 6 x^{2}$$

Short Answer

Expert verified

-6x and 6x^{2} are not like terms.

Step by step solution

- Identify the coefficients

The coefficients are the numerical parts of the terms. In this case, the coefficients are -6 and 6.

- Identify the variables

The variables are the alphabetical parts of the terms. In this case, both terms have the variable x.

- Identify the exponents of the variables

Check the exponents of the variables: -6x has x^{1} and 6x^{2} has x^{2}.

- Compare the variables and their exponents

Compare the variables and their exponents in both terms. For the terms to be like terms, they must have the same variable raised to the same power. Here, -6x has x^{1} and 6x^{2} has x^{2}, so they are not like terms.

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Key Concepts

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

coefficients

Coefficients are the numerical parts of terms. They tell us how many times the variable is multiplied. For example, in the term $-6x$, the coefficient is -6, and in $6x^2$, the coefficient is 6.

It's important to note that coefficients can be positive or negative numbers. They show how factors affect the term's size. Always look before the variable to find the coefficient.

Remember, coefficients are crucial for comparing like terms. But alone, they don't make terms like or unlike.

variables

Variables are the alphabetical parts of a term. They represent unknown or changeable values. In our example, both terms have the variable $x$.

Variables are essential because they help us see what part of the term can change. They also show us how different terms may relate. When looking for like terms, check that the variables are the same.

It's not enough for the terms to just have the same variable. Exponents are the next key factor we need to consider.

exponents

Exponents tell us how many times to multiply the variable by itself. In the term $-6x$, we have $x^1$ (which is not usually written out), and in $6x^2$, we have $x^2$.

Exponents are critical in defining like terms. To qualify as like terms, they must have the same variable raised to the same power. In this case, $-6x$ has $x^1$ and $6x^2$ has $x^2$.

Since the exponents (1 and 2) are different, $-6x$ and $6x^2$ are not like terms. Understanding and identifying exponents correctly help in solving and simplifying algebraic expressions efficiently.

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91影视

Determine if the terms are like terms. $$-6 x \quad and\quad 6 x^{2}$$

Short Answer

Step by step solution

- Identify the coefficients

- Identify the variables

- Identify the exponents of the variables

- Compare the variables and their exponents

Key Concepts

coefficients

variables

exponents

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