Problem 47 Collect like terms. $$ 9 a+1... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 11: Problem 47

Collect like terms. $$ 9 a+10 a $$

Short Answer

Expert verified

19a

Step by step solution

- Identify like terms

Identify the parts of the expression that have the same variable part. In this case, both terms are like terms since they both contain the variable 'a'.

- Combine coefficients

Add the coefficients of the like terms together. The coefficients are 9 and 10.

- Write the simplified term

Combine the coefficients by adding 9 and 10 to get 19, and then attach the common variable 'a' to the sum of the coefficients. This results in 19a.

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Key Concepts

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

algebra

Algebra is a branch of mathematics that uses symbols and letters to represent numbers and quantities. In algebra, these symbols and letters are used to express mathematical relationships and perform operations. One fundamental concept in algebra is the manipulation of algebraic expressions. This involves combining like terms, simplifying expressions, and solving equations. By learning these basic operations, you can tackle more complex algebraic problems with ease.

Symbols represent quantities.
Variables like 'a' can stand in for unknowns.
Equations show relationships between quantities.

identifying like terms

Like terms are terms that have the same variable raised to the same power. In the expression given in the exercise, both terms are 9a and 10a. These are like terms because they both contain the variable 'a' and the same exponent, which is 1. Identifying like terms is crucial for simplifying algebraic expressions.
Recognizing like terms involves:

Checking if the variables are the same.
Ensuring the exponents on these variables match.

Once you've identified the like terms, you can combine them by adding or subtracting their coefficients.

combining coefficients

Combining coefficients is the process of adding or subtracting the numerical parts of like terms. In the exercise, the coefficients are 9 and 10, attached to the variable 'a'. Combining these involves simple arithmetic.
Here's how you do it:

Add the coefficients together by calculating: 9 + 10 = 19.
Attach the common variable 'a' to this sum.

The simplified term from the example is thus 19a. This demonstrates the fundamental process of combining coefficients to simplify algebraic expressions and make calculations more straightforward.

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91影视

Collect like terms. $$ 9 a+10 a $$

Short Answer

Step by step solution

- Identify like terms

- Combine coefficients

- Write the simplified term

Key Concepts

algebra

identifying like terms

combining coefficients

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