Simplify The Expression: ( − 8 − R ) + ( 2 R − 4 (-8 - R) + (2r - 4 ( − 8 − R ) + ( 2 R − 4 ]

Introduction

In mathematics, simplifying expressions is a crucial skill that helps us to solve problems more efficiently and accurately. It involves combining like terms, removing unnecessary parentheses, and rearranging the terms to make the expression more manageable. In this article, we will focus on simplifying the given expression: $(-8 - r) + (2r - 4)$. We will use algebraic techniques to simplify the expression and provide a clear understanding of the process.

Understanding the Expression

The given expression is a combination of two terms: $(-8 - r)$ and $(2r - 4)$. To simplify the expression, we need to combine these two terms by adding or subtracting them. However, before we can do that, we need to understand the properties of the terms involved.

Properties of the Terms

The first term, $(-8 - r)$, is a linear expression that involves a constant term (-8) and a variable term (-r). The second term, $(2r - 4)$, is also a linear expression that involves a constant term (-4) and a variable term (2r).

Combining Like Terms

To simplify the expression, we need to combine like terms. Like terms are terms that have the same variable or variables raised to the same power. In this case, the like terms are the variable terms (-r and 2r) and the constant terms (-8 and -4).

Simplifying the Expression

Now that we have identified the like terms, we can simplify the expression by combining them. To do this, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate the expressions inside the parentheses.
2. Exponents: Evaluate any exponential expressions.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Step 1: Evaluate the Expressions Inside the Parentheses

The expressions inside the parentheses are $(-8 - r)$ and $(2r - 4)$. We can evaluate these expressions by simplifying the terms inside the parentheses.

$(-8 - r) = -8 - r$

$(2r - 4) = 2r - 4$

Step 2: Combine the Like Terms

Now that we have evaluated the expressions inside the parentheses, we can combine the like terms. The like terms are the variable terms (-r and 2r) and the constant terms (-8 and -4).

$(-8 - r) + (2r - 4) = -8 - r + 2r - 4$

Step 3: Simplify the Expression

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

$-8 - r + 2r - 4 = -8 + (-r + 2r) - 4$

$= -8 + r - 4$

$= -12 + r$

Conclusion

In this article, we simplified the expression $(-8 - r) + (2r - 4)$ by combining like terms and rearranging the terms. We used algebraic techniques to simplify the expression and provided a clear understanding of the process. The simplified expression is $-12 + r$, which is a linear expression that involves a constant term (-12) and a variable term (r).

Final Answer

The final answer is: $\boxed{-12 + r}$

Introduction

In our previous article, we simplified the expression $(-8 - r) + (2r - 4)$ by combining like terms and rearranging the terms. We provided a clear understanding of the process and arrived at the simplified expression: $-12 + r$. In this article, we will answer some frequently asked questions related to simplifying the expression.

Q&A

Q1: What are like terms?

A1: Like terms are terms that have the same variable or variables raised to the same power. In the expression $(-8 - r) + (2r - 4)$, the like terms are the variable terms (-r and 2r) and the constant terms (-8 and -4).

Q2: How do I identify like terms in an expression?

A2: To identify like terms in an expression, you need to look for terms that have the same variable or variables raised to the same power. You can also use the distributive property to expand the expression and then identify the like terms.

Q3: What is the order of operations (PEMDAS)?

A3: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when simplifying an expression. The order of operations is:

1. Parentheses: Evaluate the expressions inside the parentheses.
2. Exponents: Evaluate any exponential expressions.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Q4: How do I simplify an expression using the order of operations?

A4: To simplify an expression using the order of operations, you need to follow the order of operations (PEMDAS). First, evaluate the expressions inside the parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q5: What is the difference between a variable and a constant?

A5: A variable is a letter or symbol that represents a value that can change. A constant is a value that does not change. In the expression $(-8 - r) + (2r - 4)$, the variable is r and the constants are -8 and -4.

Q6: How do I simplify an expression with variables and constants?

A6: To simplify an expression with variables and constants, you need to combine the like terms. Like terms are terms that have the same variable or variables raised to the same power. You can use the distributive property to expand the expression and then combine the like terms.

Q7: What is the final answer to the expression $(-8 - r) + (2r - 4)$?

A7: The final answer to the expression $(-8 - r) + (2r - 4)$ is $-12 + r$.

Conclusion

In this article, we answered some frequently asked questions related to simplifying the expression $(-8 - r) + (2r - 4)$. We provided clear explanations and examples to help you understand the concepts. We hope this article has been helpful in clarifying any doubts you may have had.

Final Answer

The final answer is: $\boxed{-12 + r}$