Rewrite In Simplest Terms:$ -4(-6d + 3) - 4(10d + 2) }$Answer Attempt 1 Out Of 3 { \square$ $
Understanding the Problem
In this article, we will delve into the world of algebraic expressions and simplify a given equation. The equation we will be working with is ${-4(-6d + 3) - 4(10d + 2)}$. Our goal is to simplify this expression and provide a clear understanding of the steps involved.
The Importance of Simplifying Algebraic Expressions
Simplifying algebraic expressions is a crucial skill in mathematics, as it allows us to manipulate and solve equations more efficiently. By simplifying expressions, we can identify patterns and relationships between variables, making it easier to solve problems and arrive at a solution.
Step 1: Distribute the Negative Sign
The first step in simplifying the given equation is to distribute the negative sign to the terms inside the parentheses. This means that we will multiply each term inside the parentheses by -4.
Step 2: Simplify the Terms
Now that we have distributed the negative sign, we can simplify the terms inside the parentheses. We will multiply each term by -4 and then combine like terms.
Step 3: Combine Like Terms
The next step is to combine like terms. In this case, we have two terms with the variable d, and two constant terms. We will combine the like terms by adding or subtracting their coefficients.
The Final Answer
And there you have it! The simplified expression is ${-16d - 20}$. This is the final answer to the given equation.
Conclusion
Simplifying algebraic expressions is an essential skill in mathematics, and it requires a clear understanding of the steps involved. By following the steps outlined in this article, you can simplify complex expressions and arrive at a solution. Remember to distribute the negative sign, simplify the terms, and combine like terms to arrive at the final answer.
Common Mistakes to Avoid
When simplifying algebraic expressions, there are several common mistakes to avoid. These include:
- Failing to distribute the negative sign
- Not simplifying the terms inside the parentheses
- Not combining like terms
- Making errors when multiplying or adding terms
Tips and Tricks
Here are some tips and tricks to help you simplify algebraic expressions:
- Always distribute the negative sign to the terms inside the parentheses
- Simplify the terms inside the parentheses before combining like terms
- Use parentheses to group like terms and make it easier to combine them
- Check your work by plugging in values or using a calculator to verify the solution
Real-World Applications
Simplifying algebraic expressions has numerous real-world applications. These include:
- Solving equations in physics and engineering
- Modeling population growth and decay
- Analyzing data in statistics and data science
- Solving optimization problems in economics and finance
Conclusion
Frequently Asked Questions
In this article, we will address some of the most common questions related to simplifying algebraic expressions. Whether you are a student, teacher, or simply looking to improve your math skills, this guide will provide you with the answers you need.
Q: What is an algebraic expression?
A: An algebraic expression is a mathematical expression that contains variables, constants, and mathematical operations. It is a way to represent a mathematical relationship between variables and constants.
Q: Why is it important to simplify algebraic expressions?
A: Simplifying algebraic expressions is important because it allows us to manipulate and solve equations more efficiently. By simplifying expressions, we can identify patterns and relationships between variables, making it easier to solve problems and arrive at a solution.
Q: What are the steps involved in simplifying an algebraic expression?
A: The steps involved in simplifying an algebraic expression are:
- Distribute the negative sign to the terms inside the parentheses
- Simplify the terms inside the parentheses
- Combine like terms
Q: What is the difference between a variable and a constant?
A: A variable is a symbol that represents a value that can change, while a constant is a value that remains the same.
Q: How do I know when to distribute the negative sign?
A: You should distribute the negative sign when it is outside the parentheses and the expression inside the parentheses contains variables or constants.
Q: What is the order of operations?
A: The order of operations is a set of rules that tells us which operations to perform first when simplifying an algebraic expression. The order of operations is:
- Parentheses
- Exponents
- Multiplication and Division
- Addition and Subtraction
Q: How do I simplify an expression with multiple variables?
A: To simplify an expression with multiple variables, you should follow the same steps as before:
- Distribute the negative sign to the terms inside the parentheses
- Simplify the terms inside the parentheses
- Combine like terms
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
- Not simplifying the terms inside the parentheses
- Not combining like terms
- Making errors when multiplying or adding terms
Q: How can I practice simplifying algebraic expressions?
A: You can practice simplifying algebraic expressions by working through examples and exercises. You can also use online resources, such as math websites and apps, to practice and improve your skills.
Q: What are some real-world applications of simplifying algebraic expressions?
A: Simplifying algebraic expressions has numerous real-world applications, including:
- Solving equations in physics and engineering
- Modeling population growth and decay
- Analyzing data in statistics and data science
- Solving optimization problems in economics and finance
Conclusion
In conclusion, simplifying algebraic expressions is a crucial skill in mathematics, and it requires a clear understanding of the steps involved. By following the steps outlined in this article, you can simplify complex expressions and arrive at a solution. Remember to distribute the negative sign, simplify the terms, and combine like terms to arrive at the final answer. With practice and patience, you can become proficient in simplifying algebraic expressions and apply this skill to real-world problems.