Simplify The Expression By Combining Like Terms: 9.3 − 8 B + 8 B + 9 B + 5 B 9.3 - 8b + 8b + 9b + 5b 9.3 − 8 B + 8 B + 9 B + 5 B

Introduction

In algebra, combining like terms is a fundamental concept that helps simplify complex expressions. It involves adding or subtracting terms that have the same variable and exponent. In this article, we will focus on simplifying the expression $9.3 - 8b + 8b + 9b + 5b$ by combining like terms.

Understanding Like Terms

Like terms are terms that have the same variable and exponent. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ and the same exponent (which is 1). On the other hand, $2x$ and $3y$ are not like terms because they have different variables ($x$ and $y$).

Simplifying the Expression

To simplify the expression $9.3 - 8b + 8b + 9b + 5b$, we need to combine like terms. The first step is to identify the like terms in the expression.

Identifying Like Terms

The expression contains the following terms:

• $9.3$
• $-8b$
• $8b$
• $9b$
• $5b$

We can see that the terms $-8b$ and $8b$ are like terms because they both have the variable $b$ and the same exponent (which is 1). Similarly, the terms $9b$ and $5b$ are also like terms.

Combining Like Terms

Now that we have identified the like terms, we can combine them.

• The like terms $-8b$ and $8b$ can be combined as follows: $-8b + 8b = 0$. This is because when we add or subtract terms with the same variable and exponent, the result is always 0.
• The like terms $9b$ and $5b$ can be combined as follows: $9b + 5b = 14b$.

Simplifying the Expression

Now that we have combined the like terms, we can simplify the expression.

$9.3 - 8b + 8b + 9b + 5b$

$= 9.3 + 0 + 14b$

$= 9.3 + 14b$

Therefore, the simplified expression is $9.3 + 14b$.

Conclusion

In this article, we have learned how to simplify the expression $9.3 - 8b + 8b + 9b + 5b$ by combining like terms. We identified the like terms in the expression, combined them, and simplified the expression to get the final result. This is a fundamental concept in algebra that helps simplify complex expressions and solve equations.

Tips and Tricks

• When combining like terms, make sure to add or subtract the coefficients (the numbers in front of the variable) and keep the variable and exponent the same.
• If you have a term with a variable and a coefficient, make sure to multiply the coefficient by the variable when combining like terms.
• When simplifying an expression, make sure to combine like terms first and then simplify the expression.

Common Mistakes to Avoid

• Not identifying like terms correctly can lead to incorrect simplification of the expression.
• Not combining like terms correctly can lead to incorrect simplification of the expression.
• Not simplifying the expression correctly can lead to incorrect solutions to equations.

Real-World Applications

Combining like terms is a fundamental concept in algebra that has many real-world applications. For example:

• In physics, combining like terms is used to simplify complex equations that describe the motion of objects.
• In engineering, combining like terms is used to simplify complex equations that describe the behavior of electrical circuits.
• In economics, combining like terms is used to simplify complex equations that describe the behavior of economic systems.

Conclusion

Introduction

In our previous article, we discussed how to simplify the expression $9.3 - 8b + 8b + 9b + 5b$ by combining like terms. In this article, we will provide a Q&A guide to help you understand the concept of combining like terms and how to apply it in different situations.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ and the same exponent (which is 1).

Q: How do I identify like terms?

A: To identify like terms, look for terms that have the same variable and exponent. For example, in the expression $2x + 3x + 4y$, the terms $2x$ and $3x$ are like terms because they both have the variable $x$ and the same exponent (which is 1).

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients (the numbers in front of the variable) and keep the variable and exponent the same. For example, in the expression $2x + 3x$, the coefficients are $2$ and $3$, so we add them to get $5x$.

Q: What if I have a term with a variable and a coefficient, and I want to combine it with another term that has the same variable but a different coefficient?

A: In this case, you need to multiply the coefficient of the first term by the variable, and then combine it with the second term. For example, in the expression $2x + 3y$, the term $2x$ has a coefficient of $2$ and a variable of $x$. If we want to combine it with the term $3y$, we need to multiply the coefficient of $2x$ by the variable $y$ to get $6xy$, and then combine it with $3y$ to get $6xy + 3y$.

Q: What if I have a term with a variable and a coefficient, and I want to combine it with another term that has the same variable but a different exponent?

A: In this case, you cannot combine the terms because they have different exponents. For example, in the expression $2x^2 + 3x$, the term $2x^2$ has an exponent of $2$ and the term $3x$ has an exponent of $1$. You cannot combine these terms because they have different exponents.

Q: How do I simplify an expression by combining like terms?

A: To simplify an expression by combining like terms, follow these steps:

1. Identify the like terms in the expression.
2. Combine the like terms by adding or subtracting the coefficients and keeping the variable and exponent the same.
3. Simplify the expression by combining the like terms.

Q: What are some common mistakes to avoid when combining like terms?

A: Some common mistakes to avoid when combining like terms include:

• Not identifying like terms correctly
• Not combining like terms correctly
• Not simplifying the expression correctly

Q: How do I apply combining like terms in real-world situations?

A: Combining like terms is used in many real-world situations, including:

• Physics: to simplify complex equations that describe the motion of objects
• Engineering: to simplify complex equations that describe the behavior of electrical circuits
• Economics: to simplify complex equations that describe the behavior of economic systems

Conclusion

In conclusion, combining like terms is a fundamental concept in algebra that helps simplify complex expressions and solve equations. By identifying like terms, combining them, and simplifying the expression, we can get the final result. This concept has many real-world applications and is an essential tool for anyone who wants to solve equations and simplify complex expressions.