Simplify The Expression: { -8b - 3 + (-3) + (-3)$}$

Mar 10, 2025 by ADMIN 52 views

**Simplifying Algebraic Expressions: A Step-by-Step Guide**

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will focus on simplifying a specific algebraic expression: ${-8b - 3 + (-3) + (-3)}$ . We will break down the expression step by step, using basic algebraic rules and properties to arrive at the final simplified form.

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:

${-8b - 3 + (-3) + (-3)}$

This expression consists of four terms:

${-8b}$
${-3}$
${-3}$
${-3}$

Step 1: Combine Like Terms

The first step in simplifying the expression is to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two like terms: ${-3}$ and ${-3}$ . We can combine these two terms by adding their coefficients.

${-3 + (-3) = -6}$

So, the expression now becomes:

${-8b - 6 + (-3)}$

Step 2: Simplify the Expression

Now that we have combined the like terms, we can simplify the expression further. We can start by combining the constant terms. In this case, we have ${-6}$ and ${-3}$ . We can combine these two terms by adding their coefficients.

${-6 + (-3) = -9}$

So, the expression now becomes:

${-8b - 9}$

Step 3: Final Simplification

We have now simplified the expression as much as possible. The final simplified form of the expression is:

${-8b - 9}$

Conclusion

Simplifying algebraic expressions is an essential skill for any math enthusiast. By following the steps outlined in this article, we have simplified the expression ${-8b - 3 + (-3) + (-3)}$ to its final form: ${-8b - 9}$ . We hope that this article has provided a clear and concise guide to simplifying algebraic expressions.

Tips and Tricks

Here are some tips and tricks to help you simplify algebraic expressions like a pro:

Always start by combining like terms.
Use the order of operations (PEMDAS) to simplify expressions.
Simplify constant terms first.
Use parentheses to group terms and simplify expressions.

Common Mistakes to Avoid

Here are some common mistakes to avoid when simplifying algebraic expressions:

Failing to combine like terms.
Not using the order of operations (PEMDAS).
Simplifying expressions incorrectly.
Not checking for errors.

Real-World Applications

Simplifying algebraic expressions has many real-world applications. Here are a few examples:

Simplifying expressions in physics and engineering.
Solving systems of equations in economics and finance.
Simplifying expressions in computer science and programming.

Final Thoughts

Introduction

In our previous article, we explored the process of simplifying algebraic expressions. We walked through a step-by-step guide on how to simplify the expression ${-8b - 3 + (-3) + (-3)}$ . 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 combine like terms. Like terms are terms that have the same variable raised to the same power.

Q: How do I combine like terms?

A: To combine like terms, you add their coefficients. For example, if you have two like terms: ${-3x}$ and ${-2x}$ , you can combine them by adding their coefficients: ${-3x + (-2x) = -5x}$ .

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when simplifying an expression. PEMDAS stands for:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify expressions with parentheses?

A: To simplify expressions with parentheses, you need to evaluate the expression inside the parentheses first. For example, if you have the expression: ${(2x + 3) + 4}$ , you would first evaluate the expression inside the parentheses: ${2x + 3}$ , and then add 4 to the result: ${2x + 3 + 4 = 2x + 7}$ .

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

A: A variable is a letter or symbol that represents a value that can change. For example, ${x}$ is a variable. A constant is a value that does not change. For example, 5 is a constant.

Q: How do I simplify expressions with variables and constants?

A: To simplify expressions with variables and constants, you need to combine like terms. For example, if you have the expression: ${2x + 3 + 4}$ , you would first combine the constants: ${3 + 4 = 7}$ , and then add the variable term: ${2x + 7}$ .

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

A: The final step in simplifying an algebraic expression is to check for errors. Make sure that you have combined all like terms and that the expression is in its simplest form.