Problem 20 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 20

Determine if the terms are like terms. $$a^{2} b^{4} \text { and }-4 a^{2} b^{4}$$

Short Answer

Expert verified

Yes, they are like terms.

Step by step solution

Understand the Concept of Like Terms

Like terms have the exact same variables raised to the same powers. The coefficients can be different, but the variable part must match exactly.

Compare Variables and Their Exponents

Inspect the given terms: $a^{2} b^{4}$ and $-4 a^{2} b^{4}$. Both terms have the variables $a$ and $b$ raised to the powers of 2 and 4 respectively.

Ignore the Coefficients

Since like terms involve the variables and their powers, the coefficients (numbers in front of the variables) do not matter. Here, the terms are $a^{2} b^{4} $ and $-4 a^{2} b^{4}$, which only differ by their coefficients (1 and -4).

Conclusion

Because the variable parts $a^{2} b^{4}$ are identical in both terms, they are considered like terms.

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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 in mathematics to represent unknown values. In algebra, letters such as $a$, $b$, $x$, and $y$ are commonly used as variables. They can stand in for numbers we don't yet know or numbers that can change.
For example, in the terms $a^{2} b^{4}$ and $-4a^{2} b^{4}$, the letters $a$ and $b$ are the variables. The letters themselves don鈥檛 change the fact that these terms are considered 'like terms'.

Always check the variables to ensure they are the same in both terms.
Pay attention to each variable's power or exponent, which we will discuss next.

exponents

Exponents indicate how many times a variable is multiplied by itself. They are written as small numbers to the upper right of the variables. For example, in $a^{2}$, the exponent is 2, meaning $a$ is multiplied by itself: $a \times a$.

In the terms $a^{2} b^{4}$ and $-4a^{2} b^{4}$, the exponents tell us that $a$ is squared and $b$ is raised to the fourth power in both terms. This makes the exponents vital in determining like terms because:

Both variables must be raised to the exact same exponents for the terms to be considered alike.
Even if the variables are the same but the exponents differ, the terms are not considered like terms.

coefficients

Coefficients are the numbers in front of the variables and their exponents. They indicate how many times the variable or the expression should be counted. For example, in the term $3x$, the coefficient is 3.

In $a^{2} b^{4}$ and $-4a^{2} b^{4}$, the coefficients are 1 and -4 respectively.

Even though the coefficients are different, it doesn't affect whether the terms are 'like terms'.
The focus should remain on whether the variables and their exponents match.

The conclusion is that, despite different coefficients, these terms are like terms because their variable parts $a^{2} b^{4}$ are exactly the same.

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91影视

Determine if the terms are like terms. $$a^{2} b^{4} \text { and }-4 a^{2} b^{4}$$

Short Answer

Step by step solution

Understand the Concept of Like Terms

Compare Variables and Their Exponents

Ignore the Coefficients

Conclusion

Key Concepts

variables

exponents

coefficients

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