Add The Following Expression: ( − 9 B − 7 ) + ( − 8 B − 9 (-9b - 7) + (-8b - 9 ( − 9 B − 7 ) + ( − 8 B − 9 ]

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill for any math enthusiast. In this article, we will focus on simplifying the given expression: $(-9b - 7) + (-8b - 9)$. We will break down the process into manageable steps, making it easy to understand and follow along.

Understanding the Expression

Before we dive into simplifying the expression, let's take a closer look at what we're dealing with. The given expression is a combination of two terms, each containing a variable (b) and a constant. The first term is $-9b - 7$, and the second term is $-8b - 9$. Our goal is to simplify this expression by combining like terms.

Step 1: Distribute the Negative Sign

The first step in simplifying the expression is to distribute the negative sign to each term inside the parentheses. This will help us to combine like terms more easily.

$(-9b - 7) + (-8b - 9)$

Distributing the negative sign, we get:

$-9b - 7 - 8b - 9$

Step 2: Combine Like Terms

Now that we have distributed the negative sign, we can combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two terms with the variable b, and two terms with constants.

$-9b - 7 - 8b - 9$

Combining the like terms, we get:

$-17b - 16$

Step 3: Simplify the Expression

We have now simplified the expression by combining like terms. The final simplified expression is:

$-17b - 16$

Conclusion

Simplifying algebraic expressions is an essential skill for any math enthusiast. By following the steps outlined in this article, we have successfully simplified the given expression: $(-9b - 7) + (-8b - 9)$. Remember to always distribute the negative sign and combine like terms to simplify expressions.

Tips and Tricks

• Always distribute the negative sign to each term inside the parentheses.
• Combine like terms by adding or subtracting the coefficients of the variables.
• Simplify the expression by combining like terms and eliminating any unnecessary parentheses.

Common Mistakes to Avoid

• Failing to distribute the negative sign to each term inside the parentheses.
• Not combining like terms, resulting in an unsimplified expression.
• Not simplifying the expression by eliminating unnecessary parentheses.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications. For example, in physics, algebraic expressions are used to describe the motion of objects. In engineering, algebraic expressions are used to design and optimize systems. In economics, algebraic expressions are used to model and analyze economic systems.

Final Thoughts

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Introduction

In our previous article, we explored the process of simplifying algebraic expressions. We broke down the steps involved in simplifying the expression: $(-9b - 7) + (-8b - 9)$. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q&A

Q: What is the first step in simplifying an algebraic expression?

A: The first step in simplifying an algebraic expression is to distribute the negative sign to each term inside the parentheses.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, in the expression $-9b - 7 - 8b - 9$, the terms $-9b$ and $-8b$ are like terms because they both have the variable b.

Q: How do I combine like terms?

A: To combine like terms, you add or subtract the coefficients of the variables. For example, in the expression $-9b - 7 - 8b - 9$, you combine the like terms $-9b$ and $-8b$ by adding their coefficients: $-9b - 8b = -17b$.

Q: What is the difference between a coefficient and a variable?

A: A coefficient is a number that is multiplied by a variable. For example, in the expression $-9b$, the coefficient is $-9$ and the variable is $b$. A variable is a letter or symbol that represents a value that can change.

Q: Can I simplify an expression with multiple variables?

A: Yes, you can simplify an expression with multiple variables. To do this, you need to combine like terms, just like you would with a single variable. For example, in the expression $-9a + 7b - 8a - 9b$, you combine the like terms $-9a$ and $-8a$ by adding their coefficients: $-9a - 8a = -17a$. Then, you combine the like terms $7b$ and $-9b$ by adding their coefficients: $7b - 9b = -2b$.

Q: How do I know if an expression is simplified?

A: An expression is simplified when there are no like terms left to combine. For example, in the expression $-17b - 16$, there are no like terms left to combine, so the expression is simplified.

Q: Can I simplify an expression with parentheses?

A: Yes, you can simplify an expression with parentheses. To do this, you need to distribute the negative sign to each term inside the parentheses, just like you would with a single term. For example, in the expression $(-9b - 7) + (-8b - 9)$, you distribute the negative sign to each term inside the parentheses: $-9b - 7 - 8b - 9$.

Q: What are some common mistakes to avoid when simplifying algebraic expressions?

A: Some common mistakes to avoid when simplifying algebraic expressions include:

• Failing to distribute the negative sign to each term inside the parentheses.
• Not combining like terms, resulting in an unsimplified expression.
• Not simplifying the expression by eliminating unnecessary parentheses.

Conclusion

Simplifying algebraic expressions is an essential skill for any math enthusiast. By following the steps outlined in this article and answering the frequently asked questions, you will become proficient in simplifying algebraic expressions and applying them to real-world problems.

Tips and Tricks

• Always distribute the negative sign to each term inside the parentheses.
• Combine like terms by adding or subtracting the coefficients of the variables.
• Simplify the expression by combining like terms and eliminating any unnecessary parentheses.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications. For example, in physics, algebraic expressions are used to describe the motion of objects. In engineering, algebraic expressions are used to design and optimize systems. In economics, algebraic expressions are used to model and analyze economic systems.

Final Thoughts

Simplifying algebraic expressions is a crucial skill for any math enthusiast. By following the steps outlined in this article and answering the frequently asked questions, you will become proficient in simplifying algebraic expressions and applying them to real-world problems. With practice and patience, you will become proficient in simplifying algebraic expressions and applying them to real-world problems.