Problem 29 In the following exercises, add ... [FREE SOLUTION]

Chapter 5: Problem 29

In the following exercises, add or subtract the monomials. Add: \(4 a,-3 b,-8 a\)

Short Answer

Expert verified

-4a - 3b

Step by step solution

Identify like terms

First, identify the like terms in the expression. Here, the terms are 1. 4a2. -3b3. -8aNotice that 4a and -8a are like terms because they both have the variable 'a'.

Combine like terms

Next, combine the like terms. Add together the coefficients of the like terms:4a - 8a = (4 - 8)a = -4a

Write the simplified expression

Now, write the simplified expression including the term that is not like the others:-4a - 3b

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Key Concepts

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

like terms

In algebra, 'like terms' are terms that have the same variables raised to the same power. For instance, in the expression given in the exercise, the terms 4a and -8a are like terms because they both contain the variable 'a'. The coefficient in front of the variable does not need to be the same. Here鈥檚 how to spot them easily:

Focus on the variable part of each term
Terms with identical variable parts are like terms

Even if terms have different coefficients, they are still considered like terms as long as their variable parts match.

combining like terms

Once like terms are identified, the next step is to combine them. Combining like terms means adding or subtracting the coefficients of those like terms while keeping the variable part unchanged. From the exercise:

4a and -8a are like terms, since they both contain 'a'
Add their coefficients: 4 and -8

This is calculated as follows:
\[ 4a - 8a = (4 - 8)a = -4a \]
The variable 'a' stays the same, but the coefficients are combined into -4. Remember that you only focus on combining coefficients, not the variable part.

coefficients

In any mathematical term involving a variable, the number in front of that variable is called the 'coefficient'. The exercise shows an example with different coefficients. Here are some important points about coefficients:

They tell us how many times the variable is to be counted
They can be positive, negative, or even fractions

In the provided problem, the coefficients are 4, -3, and -8. When combining like terms, only the coefficients change; the variable part remains the same. Understanding the role of coefficients helps you confidently simplify expressions by focusing on these numbers.

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91影视

In the following exercises, add or subtract the monomials. Add: \(4 a,-3 b,-8 a\)

Short Answer

Step by step solution

Identify like terms

Combine like terms

Write the simplified expression

Key Concepts

like terms

combining like terms

coefficients

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