Simplify The Expression \left(5 E^2-6 E+7\right)-\left(4 E^2-6 E-2\right ].A. 9 E 2 + 9 9 E^2+9 9 E 2 + 9 B. E 2 + 9 E^2+9 E 2 + 9 C. 9 E 2 − 12 E + 5 9 E^2-12 E+5 9 E 2 − 12 E + 5 D. E 2 − 12 E + 9 E^2-12 E+9 E 2 − 12 E + 9

Introduction

In this article, we will simplify the given expression $\left(5 e^2-6 e+7\right)-\left(4 e^2-6 e-2\right)$. This involves combining like terms and applying the rules of algebra to arrive at the final simplified expression.

Understanding the Expression

The given expression is a combination of two terms, each containing exponential and linear terms. The first term is $5 e^2-6 e+7$, and the second term is $4 e^2-6 e-2$. To simplify the expression, we need to combine like terms, which involves adding or subtracting terms with the same variable and exponent.

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 parentheses. This will change the sign of each term inside the parentheses.

$\left(5 e^2-6 e+7\right)-\left(4 e^2-6 e-2\right)$

$= 5 e^2-6 e+7 + \left(-4 e^2+6 e+2\right)$

Step 2: Combine Like Terms

Now that we have distributed the negative sign, we can combine like terms. This involves adding or subtracting terms with the same variable and exponent.

$= 5 e^2-6 e+7 -4 e^2+6 e+2$

$= (5 e^2 - 4 e^2) + (-6 e + 6 e) + (7 + 2)$

Step 3: Simplify the Expression

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

$= e^2 + 9$

Conclusion

In this article, we simplified the given expression $\left(5 e^2-6 e+7\right)-\left(4 e^2-6 e-2\right)$ by distributing the negative sign and combining like terms. The final simplified expression is $e^2 + 9$.

Answer

The correct answer is B. $e^2+9$.

Discussion

This problem involves applying the rules of algebra to simplify an expression. The key concept is to combine like terms, which involves adding or subtracting terms with the same variable and exponent. This problem requires a strong understanding of algebraic expressions and the ability to apply the rules of algebra to simplify complex expressions.

Related Topics

• Simplifying algebraic expressions
• Combining like terms
• Distributing negative signs
• Evaluating expressions

Practice Problems

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

Conclusion

$$$$

Introduction

In our previous article, we simplified the expression $\left(5 e^2-6 e+7\right)-\left(4 e^2-6 e-2\right)$ by distributing the negative sign and combining like terms. In this article, we will provide a Q&A guide to help you understand the concept of simplifying algebraic expressions.

Q: What is the first step in simplifying an algebraic expression?

A: The first step in simplifying an algebraic expression is to distribute the negative sign to the terms inside the second parentheses. This will change the sign of each term inside the parentheses.

Q: What is the difference between combining like terms and distributing the negative sign?

A: Combining like terms involves adding or subtracting terms with the same variable and exponent. Distributing the negative sign involves changing the sign of each term inside the parentheses.

Q: How do I know which terms to combine?

A: To combine like terms, you need to identify the terms with the same variable and exponent. For example, in the expression $\left(5 e^2-6 e+7\right)-\left(4 e^2-6 e-2\right)$, the terms $5 e^2$ and $-4 e^2$ are like terms because they have the same variable and exponent.

Q: What is the final simplified expression for the given problem?

A: The final simplified expression for the given problem is $e^2 + 9$.

Q: What are some common mistakes to avoid when simplifying algebraic expressions?

A: Some common mistakes to avoid when simplifying algebraic expressions include:

• Not distributing the negative sign correctly
• Not combining like terms correctly
• Not evaluating the expression correctly

Q: How can I practice simplifying algebraic expressions?

A: You can practice simplifying algebraic expressions by working on practice problems, such as the ones listed below:

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

Q: What are some real-world applications of simplifying algebraic expressions?

A: Simplifying algebraic expressions has many real-world applications, including:

• Solving systems of equations
• Finding the maximum or minimum value of a function
• Modeling real-world phenomena, such as population growth or chemical reactions

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 distributing the negative sign, combining like terms, and evaluating expressions. We also provided practice problems and real-world applications to help you reinforce your understanding of the concept.

Practice Problems

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

Real-World Applications

• Solving systems of equations
• Finding the maximum or minimum value of a function
• Modeling real-world phenomena, such as population growth or chemical reactions

Additional Resources

• Algebra textbooks
• Online resources, such as Khan Academy or Mathway
• Practice problems and worksheets

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 distributing the negative sign, combining like terms, and evaluating expressions. We also provided practice problems and real-world applications to help you reinforce your understanding of the concept.