Problem 66 Combine the like terms. $$13 x... [FREE SOLUTION]

91影视

Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 3: Problem 66

Combine the like terms. $$13 x y^{2}+8 x y^{2}$$

Short Answer

Expert verified

21虫测虏

Step by step solution

Identify Like Terms

Like terms are terms that have the same variables raised to the same power. In the expression, 13xy虏 and 8xy虏 are like terms because both terms have the variables xy raised to the second power.

Add Coefficients

To combine the like terms, add their coefficients. The coefficients of the terms 13xy虏 and 8xy虏 are 13 and 8, respectively. So, 13 + 8 = 21.

Write the Combined Term

After adding the coefficients, write the product with the common variable and exponent. Hence, the combined term is 21虫测虏.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

coefficients

In mathematics, a coefficient is the numerical part of a term that is multiplied by the variable(s). For instance, in the term 13xy虏, the number 13 is the coefficient. Coefficients are essential because they dictate how many times the variables are counted.

When combining like terms, we focus on the coefficients. In this example, we have two terms: 13xy虏 and 8xy虏. Both terms have the same variables raised to the same powers. The coefficients are 13 and 8.

By adding these coefficients together, we get: 13 + 8 = 21. Combining like terms means we sum the coefficients and keep the variable part unchanged. Thus, the new term is 21虫测虏.

variables

Variables are symbols (often letters) that represent numbers in expressions and equations. In our example, the variables are x and y.

Variables can stand for any value. When combining like terms, we look for terms with the exact same variables. Here, both terms have xy虏. If the variable parts differ, the terms are not 'like terms' and can't be combined directly.

In combining like terms, such as in 13xy虏 and 8xy虏, we ensure their variables match. When they do, we simply add or subtract the coefficients, keeping the variables intact. The result 21虫测虏 still has the variables xy虏 unchanged from the original terms.

exponents

Exponents indicate how many times a number (base) is multiplied by itself. In the term xy虏, y is raised to the power of 2, meaning y is multiplied by itself: y * y.

When we have terms like 13xy虏 and 8xy虏, their exponents also must match to be combined. Both terms have y raised to the power of 2 (y虏), making them like terms.

When combining like terms, the exponents on the variables remain unchanged; only their coefficients are added. So, in 13xy虏 and 8xy虏, after adding the coefficients, we have 21虫测虏, with the exponent of y still being 2. This is key to simplifying expressions correctly.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Combine the like terms. $$13 x y^{2}+8 x y^{2}$$

Short Answer

Step by step solution

Identify Like Terms

Add Coefficients

Write the Combined Term

Key Concepts

coefficients

variables

exponents

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Logic and Functions

Applied Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.