Select The Correct Answer.What Is The Simplified Form Of This Expression? \left(5x^2 + 2x + 11\right) - \left(7 + 4x - 2x^2\right ]A. 3 X 2 − 2 X + 4 3x^2 - 2x + 4 3 X 2 − 2 X + 4 B. 3 X 2 + 6 X + 4 3x^2 + 6x + 4 3 X 2 + 6 X + 4 C. 9 − 2 X − 2 X 2 9 - 2x - 2x^2 9 − 2 X − 2 X 2 D. 7 X 2 − 2 X + 4 7x^2 - 2x + 4 7 X 2 − 2 X + 4

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 algebraic expression, and we will provide a step-by-step guide on how to do it.

The Expression to Simplify

The expression we will be simplifying is:

$\left(5x^2 + 2x + 11\right) - \left(7 + 4x - 2x^2\right)$

Step 1: Distribute the Negative Sign

The first step in simplifying this expression is to distribute the negative sign to the terms inside the second set of parentheses. This means that we will change the sign of each term inside the second set of parentheses.

$\left(5x^2 + 2x + 11\right) - \left(7 + 4x - 2x^2\right) = \left(5x^2 + 2x + 11\right) + \left(-7 - 4x + 2x^2\right)$

Step 2: Combine Like Terms

The next step 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 terms with the variable $x^2$, two terms with the variable $x$, and two constant terms.

$\left(5x^2 + 2x + 11\right) + \left(-7 - 4x + 2x^2\right) = \left(5x^2 + 2x^2\right) + \left(2x - 4x\right) + \left(11 - 7\right)$

Step 3: Simplify Each Group of Like Terms

Now that we have combined like terms, we can simplify each group of like terms.

$\left(5x^2 + 2x^2\right) + \left(2x - 4x\right) + \left(11 - 7\right) = 7x^2 - 2x + 4$

Conclusion

In conclusion, the simplified form of the expression is $7x^2 - 2x + 4$. This is the correct answer.

Answer Options

Here are the answer options:

• A. $3x^2 - 2x + 4$
• B. $3x^2 + 6x + 4$
• C. $9 - 2x - 2x^2$
• D. $7x^2 - 2x + 4$

Which Answer is Correct?

Based on our step-by-step guide, we can see that the correct answer is:

• D. $7x^2 - 2x + 4$

Why is this the Correct Answer?

This is the correct answer because we followed the order of operations and combined like terms correctly. We also simplified each group of like terms to get the final answer.

Tips and Tricks

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

• Always follow the order of operations (PEMDAS).
• Combine like terms by adding or subtracting coefficients.
• Simplify each group of like terms to get the final answer.

Practice Problems

Here are some practice problems to help you practice simplifying algebraic expressions:

• Simplify the expression: $\left(2x^2 + 3x + 1\right) - \left(4x - 2x^2 + 3\right)$
• Simplify the expression: $\left(x^2 + 2x - 1\right) + \left(3x - 2x^2 + 1\right)$

Conclusion

Introduction

In our previous article, we provided a step-by-step guide on how to simplify algebraic expressions. In this article, we will provide a Q&A guide to help you understand the concepts and techniques involved in 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 such as addition, subtraction, multiplication, and division.

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:

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: 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 algebraic expression?

A: To simplify an algebraic expression, follow these steps:

1. Distribute any negative signs to the terms inside the parentheses.
2. Combine like terms by adding or subtracting coefficients.
3. Simplify each group of like terms to get the final answer.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2x^2$ and $3x^2$ are like terms because they both have the variable $x$ raised to the power of 2.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the like terms. For example, $2x^2 + 3x^2 = 5x^2$.

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

A: A coefficient is a number that is multiplied by a variable. 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, follow these steps:

1. Evaluate the expression inside the parentheses first.
2. Simplify the expression inside the parentheses.
3. Combine like terms and simplify the expression.

Q: What is the difference between a positive and negative coefficient?

A: A positive coefficient is a number that is multiplied by a variable, while a negative coefficient is a number that is multiplied by a variable and has a negative sign.

Q: How do I simplify an expression with exponents?

A: To simplify an expression with exponents, follow these steps:

1. Evaluate any exponential expressions first.
2. Simplify the expression.
3. Combine like terms and simplify the expression.

Q: What is the difference between a rational and irrational exponent?

A: A rational exponent is an exponent that is a fraction, while an irrational exponent is an exponent that is not a fraction.

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill for students and professionals alike. By following the order of operations and combining like terms correctly, we can simplify complex expressions and get the final answer. We hope this Q&A guide has been helpful in providing a better understanding of the concepts and techniques involved in simplifying algebraic expressions.

Practice Problems

Here are some practice problems to help you practice simplifying algebraic expressions:

• Simplify the expression: $\left(2x^2 + 3x + 1\right) - \left(4x - 2x^2 + 3\right)$
• Simplify the expression: $\left(x^2 + 2x - 1\right) + \left(3x - 2x^2 + 1\right)$
• Simplify the expression: $\left(5x^2 + 2x + 11\right) - \left(7 + 4x - 2x^2\right)$

Answer Key

Here are the answers to the practice problems:

• Simplify the expression: $\left(2x^2 + 3x + 1\right) - \left(4x - 2x^2 + 3\right) = 4x^2 - x + 4$
• Simplify the expression: $\left(x^2 + 2x - 1\right) + \left(3x - 2x^2 + 1\right) = -x^2 + 5x$
• Simplify the expression: $\left(5x^2 + 2x + 11\right) - \left(7 + 4x - 2x^2\right) = 7x^2 - 2x + 4$