Problem 6 Simplify each expression by comb... [FREE SOLUTION]

Chapter 3: Problem 6

Simplify each expression by combining like terms. $$ 5 b-8 b-b $$

Short Answer

Expert verified

The simplified expression is $-4b$.

Step by step solution

Identify Like Terms

In the expression $5b - 8b - b$, the like terms are the terms that have the same variable raised to the same power. Here, all three terms $5b$, $-8b$, and $-b$ are like terms because they all contain the variable $b$ raised to the first power.

Combine Like Terms

To simplify the expression, add or subtract the coefficients of the like terms. The coefficients in this case are 5, -8, and -1 (for $-b$). So we calculate: \[5 - 8 - 1 = -4\]

Write the Simplified Expression

With the coefficients combined, the simplified expression is the term with the combined coefficient and the variable $b$. Thus, the expression simplifies to:$-4b$.

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Key Concepts

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

Simplifying Expressions

Simplifying expressions is a crucial skill in algebra. It involves reducing a mathematical expression to its simplest form. The process makes it easier to work with and understand. When you simplify an expression, the goal is to have it consist of as few terms as possible. This makes it more manageable.Simplifying usually involves:

Combining like terms
Eliminating unnecessary parts

In our original exercise, simplifying helps us turn the cumbersome expression $5b - 8b - b$ into a single term $-4b$. So next time you see a long expression, look for opportunities to simplify and make your work easier.

Identifying Like Terms

Like terms are the building blocks of simplification. They are terms in an equation or expression that have the same variable parts. This means the variables have to be identical and raised to the same power.For example:

$3x$ and $-5x$ are like terms
$x^2$ and $4x^2$ are like terms
However, $x$ and $x^2$ are not like terms

In our exercise $5b - 8b - b$, all terms are like terms. They each have the variable $b$ raised to the first power. Once you identify like terms, you can proceed to combine them. This step is a foundation of simplifying expressions.

Coefficients

Coefficients are the numerical parts of terms that help us simplify expressions. They tell us how much of a variable we have. For example, in the term $5b$, "5" is the coefficient.To effectively combine like terms:

Find the coefficients of each term
Add or subtract the coefficients as needed

In our expression, $5b$ has a coefficient of 5, $-8b$ has a coefficient of -8, and $-b$ has a coefficient of -1. After combining these coefficients, we simplify the expression to $-4b$. Remember, handling coefficients correctly is key to accurate simplification.

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91影视

Simplify each expression by combining like terms. $$ 5 b-8 b-b $$

Short Answer

Step by step solution

Identify Like Terms

Combine Like Terms

Write the Simplified Expression

Key Concepts

Simplifying Expressions

Identifying Like Terms

Coefficients

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