Which Expression Is Equivalent To \left(2r^2 + R - 1\right) - \left(3r^2 + 4r - 5\right ]?A. 5 R 2 − 3 R + 4 5r^2 - 3r + 4 5 R 2 − 3 R + 4 B. 5 R 2 + 5 R − 6 5r^2 + 5r - 6 5 R 2 + 5 R − 6 C. − R 2 − 3 R + 4 -r^2 - 3r + 4 − R 2 − 3 R + 4 D. − R 2 + 5 R − 6 -r^2 + 5r - 6 − R 2 + 5 R − 6

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, which involves combining like terms and applying the order of operations. We will also explore the importance of simplifying algebraic expressions and provide a step-by-step guide on how to do it.

What is an Algebraic Expression?

An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way of representing a mathematical relationship between variables and constants. Algebraic expressions can be simple or complex, and they can be used to solve equations, inequalities, and other mathematical problems.

The Order of Operations

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 as follows:

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

Simplifying the Given Expression

Now that we have a basic understanding of algebraic expressions and the order of operations, let's simplify the given expression:

$\left(2r^2 + r - 1\right) - \left(3r^2 + 4r - 5\right)$

To simplify this expression, we need to combine like terms and apply the order of operations.

Step 1: Distribute the Negative Sign

The first step in simplifying the expression is to distribute the negative sign to the terms inside the second set of parentheses.

$\left(2r^2 + r - 1\right) - \left(3r^2 + 4r - 5\right)$

$= 2r^2 + r - 1 - 3r^2 - 4r + 5$

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 and exponent.

$= 2r^2 - 3r^2 + r - 4r - 1 + 5$

$= -r^2 - 3r + 4$

Step 3: Check the Answer

Now that we have simplified the expression, let's check our answer by plugging it back into the original expression.

$\left(2r^2 + r - 1\right) - \left(3r^2 + 4r - 5\right)$

$= -r^2 - 3r + 4$

$= -r^2 - 3r + 4$

The answer checks out!

Conclusion

Simplifying algebraic expressions is an essential skill for any math enthusiast. By following the order of operations and combining like terms, we can simplify even the most complex expressions. In this article, we simplified a specific algebraic expression and provided a step-by-step guide on how to do it. We also explored the importance of simplifying algebraic expressions and provided a brief overview of algebraic expressions and the order of operations.

Which Expression is Equivalent to the Given Expression?

Now that we have simplified the given expression, let's compare it to the answer choices.

A. $5r^2 - 3r + 4$

B. $5r^2 + 5r - 6$

C. $-r^2 - 3r + 4$

D. $-r^2 + 5r - 6$

The correct answer is C. $-r^2 - 3r + 4$. This is the simplified expression that we obtained in the previous section.

Final Answer

Introduction

In our previous article, we explored the concept of simplifying algebraic expressions and provided a step-by-step guide on how to do it. In this article, we will answer some frequently asked questions related to simplifying algebraic expressions.

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 as follows:

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

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to follow these steps:

1. Distribute the negative sign to the terms inside the second set of parentheses.
2. Combine like terms.
3. Check the answer by plugging it back into the original expression.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, 2x and 4x are like terms because they both have the variable x and the same exponent.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, if you have 2x + 4x, you can combine them by adding the coefficients: 2x + 4x = 6x.

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. A constant is a value that does not change.

Q: How do I simplify an expression with parentheses?

A: To simplify an expression with parentheses, you need to evaluate the expression inside the parentheses first. Then, you can simplify the expression outside the parentheses.

Q: Can I simplify an expression with exponents?

A: Yes, you can simplify an expression with exponents. To simplify an expression with exponents, you need to evaluate the exponential expressions first. Then, you can simplify the expression.

Q: How do I check my answer?

A: To check your answer, you need to plug it back into the original expression. If the answer checks out, then you have simplified the expression correctly.

Conclusion

Simplifying algebraic expressions is an essential skill for any math enthusiast. By following the order of operations and combining like terms, we can simplify even the most complex expressions. In this article, we answered some frequently asked questions related to simplifying algebraic expressions and provided a brief overview of the concept.

Additional Resources

If you want to learn more about simplifying algebraic expressions, here are some additional resources that you can use:

• Khan Academy: Simplifying Algebraic Expressions
• Mathway: Simplifying Algebraic Expressions
• Wolfram Alpha: Simplifying Algebraic Expressions

Final Answer

The final answer is that simplifying algebraic expressions is an essential skill for any math enthusiast. By following the order of operations and combining like terms, we can simplify even the most complex expressions.