Select The Correct Answer.What Is The Simplified Form Of This Expression? \left(4x^2-3x+8\right)-\left(2x^2+2x-5\right ]A. 4 X 2 − 5 X + 13 4x^2-5x+13 4 X 2 − 5 X + 13 B. 2 X 2 − 5 X + 13 2x^2-5x+13 2 X 2 − 5 X + 13 C. 2 X 2 − 5 X + 3 2x^2-5x+3 2 X 2 − 5 X + 3 D. 2 X 2 − X + 3 2x^2-x+3 2 X 2 − X + 3

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying a specific type of algebraic expression, which involves combining like terms and performing arithmetic operations. We will use a step-by-step approach to simplify the given expression and arrive at the correct answer.

The Expression to Simplify

The given expression is:

$\left(4x^2-3x+8\right)-\left(2x^2+2x-5\right)$

Our goal is to simplify this expression by combining like terms and performing arithmetic 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. This will change the sign of each term inside the parentheses.

$\left(4x^2-3x+8\right)-\left(2x^2+2x-5\right) = 4x^2-3x+8-2x^2-2x+5$

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 raised to the same power. In this case, we have two terms with the variable $x^2$, two terms with the variable $x$, and two constant terms.

$4x^2-3x+8-2x^2-2x+5 = (4x^2-2x^2) + (-3x-2x) + (8+5)$

Step 3: Simplify Each Group of Like Terms

Now we can simplify each group of like terms.

$(4x^2-2x^2) = 2x^2$

$(-3x-2x) = -5x$

$(8+5) = 13$

Step 4: Write the Simplified Expression

Now that we have simplified each group of like terms, we can write the simplified expression.

$2x^2-5x+13$

Conclusion

In this article, we simplified the given algebraic expression by combining like terms and performing arithmetic operations. We used a step-by-step approach to arrive at the correct answer. The simplified expression is:

$2x^2-5x+13$

This expression is the correct answer to the given problem.

Answer

The correct answer is:

• A. $4x^2-5x+13$ is incorrect
• B. $2x^2-5x+13$ is correct
• C. $2x^2-5x+3$ is incorrect
• D. $2x^2-x+3$ is incorrect

Final Answer

$$

Introduction

In our previous article, we simplified a given algebraic expression by combining like terms and performing arithmetic operations. In this article, we will provide a Q&A guide to help you understand the concept of simplifying algebraic expressions.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way to represent a mathematical relationship between variables and constants.

Q: What is a like term?

A: A like term is a term that has the same variable raised to the same power. For example, $2x^2$ and $4x^2$ are like terms because they both have the variable $x$ raised to the power of 2.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms and perform arithmetic operations. Here are the steps:

1. Distribute the negative sign to the terms inside the second set of parentheses.
2. Combine like terms by adding or subtracting the coefficients of the like terms.
3. Simplify each group of like terms by performing arithmetic operations.
4. Write the simplified expression.

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 identify like terms in an algebraic expression?

A: To identify like terms in an algebraic expression, you need to look for terms that have the same variable raised to the same power. For example, in the expression $2x^2 + 4x^2$, the terms $2x^2$ and $4x^2$ are like terms because they both have the variable $x$ raised to the power of 2.

Q: Can I simplify an algebraic expression by combining unlike terms?

A: No, you cannot simplify an algebraic expression by combining unlike terms. Unlike terms are terms that have different variables or different powers of the same variable. For example, $2x^2$ and $3y^2$ are unlike terms because they have different variables.

Q: How do I know when to use a negative sign when simplifying an algebraic expression?

A: When simplifying an algebraic expression, you need to use a negative sign when distributing the negative sign to the terms inside the second set of parentheses. This will change the sign of each term inside the parentheses.

Q: Can I simplify an algebraic expression by using a calculator?

A: Yes, you can simplify an algebraic expression by using a calculator. However, it is always best to simplify the expression by hand to ensure that you understand the concept and to avoid making mistakes.

Conclusion

In this article, we provided a Q&A guide to help you understand the concept of simplifying algebraic expressions. We covered topics such as like terms, variables, constants, and arithmetic operations. We hope that this guide has been helpful in simplifying your understanding of algebraic expressions.

Final Answer

The final answer is $\boxed{2x^2-5x+13}$.