Problem 18 Determine if the two terms are l... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 3: Problem 18

Determine if the two terms are like terms or unlike terms. If they are unlike terms, explain why. $$8 b, 12 b$$

Short Answer

Expert verified

The terms 8b and 12b are like terms.

Step by step solution

Identify the Variables

Look at the variables in each term. For the first term, the variable is $ b $. For the second term, the variable is also $ b $.

Check the Variables' Exponents

Ensure the variables have the same exponents. In both terms, the exponent of $ b $ is implicitly 1. That means both terms have $ b^1 $.

Compare the Variables and Their Exponents

Since both terms have the same variable $ b $ and the same exponent 1, the terms 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 to represent unknown values in mathematical expressions. They can be any letter from the alphabet, and in this exercise, the variable is $ b $. A key thing to remember about variables is that they can stand for any number. In our exercise, the presence of the same variable in both terms means we can compare them to see if they are alike.
The core idea is to recognize the variable involved. If you have the same variable (like $ b $ in our case), you can proceed to check if these variables have the same exponents.

Exponents

Exponents denote how many times a number (the base) is multiplied by itself. For example, in $3^2$, 3 is the base, and 2 is the exponent, meaning $3 \times 3 = 9$. Exponents are crucial in determining whether terms are like terms. In our problem, each $ b $ has an implicit exponent of 1 (since $ b = b^1 $).
If two terms have the same variable but different exponents, they are unlike terms because the exponent changes the value significantly. So, remember: same variable and same exponent are needed for like terms.

Simplifying Expressions

Simplifying expressions involves combining like terms to make an expression easier to work with. Like terms have the same variables raised to the same power, as we've learned. For example: $8b + 12b$ are like terms because they both have the variable $ b $ with the same exponent.
When simplifying, you combine these using basic arithmetic: $ 8b + 12b = (8 + 12)b = 20b $. This consolidation makes further math operations simpler.
Simplifying helps reduce complexity in longer expressions and is fundamental in algebraic manipulations. Always verify like terms before combining.

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91影视

Determine if the two terms are like terms or unlike terms. If they are unlike terms, explain why. $$8 b, 12 b$$

Short Answer

Step by step solution

Identify the Variables

Check the Variables' Exponents

Compare the Variables and Their Exponents

Key Concepts

Variables

Exponents

Simplifying Expressions

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