Simplify The Expression: $\left(x^2-x+8\right)+\left(10x^2+7\right$\]A. $10x^2-x+1$ B. $11x^2-x+1$ C. $10x^2-x+15$ D. $11x^2-x+15$

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Introduction

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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 type of algebraic expression, namely the combination of two or more terms. We will use the given expression $\left(x^2-x+8\right)+\left(10x^2+7\right)$ as an example to demonstrate the step-by-step process of simplifying algebraic expressions.

Understanding the Expression

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Before we begin simplifying the expression, let's take a closer look at what we're dealing with. The given expression consists of two terms: $\left(x^2-x+8\right)$ and $\left(10x^2+7\right)$. Our goal is to combine these two terms into a single expression.

Combining Like Terms

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The first step in simplifying the expression 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 $x$ raised to the power of 2: $x^2$ and $10x^2$. We can combine these two terms by adding their coefficients.

# Define the coefficients of the like terms
coefficient_x2 = 1
coefficient_10x2 = 10

# Combine the like terms
combined_x2 = coefficient_x2 + coefficient_10x2
print(combined_x2)

The output of the above code will be 11, which is the combined coefficient of the $x^2$ term.

Simplifying the Expression

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Now that we have combined the like terms, we can simplify the expression by adding the remaining terms. The expression now becomes:

$$11x^2 - x + 8 + 7$$

We can simplify this expression further by combining the constant terms:

$$11x^2 - x + 15$$

Conclusion

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In conclusion, simplifying algebraic expressions is an essential skill for any math enthusiast. By following the step-by-step process outlined in this article, we can simplify complex expressions and arrive at a simplified form. In this case, we simplified the expression $\left(x^2-x+8\right)+\left(10x^2+7\right)$ to $11x^2 - x + 15$.

Final Answer

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The final answer to the given problem is:

$11x^2 - x + 15$

This answer matches option D, which is the correct answer.

Frequently Asked Questions

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Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or different powers of the same variable.

Q: How do I combine like terms?

A: To combine like terms, add their coefficients.

Q: What is the simplified form of the expression $\left(x^2-x+8\right)+\left(10x^2+7\right)$?

A: The simplified form of the expression is $11x^2 - x + 15$.

Additional Resources

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For more information on simplifying algebraic expressions, check out the following resources:

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

Conclusion

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Simplifying algebraic expressions is an essential skill for any math enthusiast. By following the step-by-step process outlined in this article, we can simplify complex expressions and arrive at a simplified form. In this case, we simplified the expression $\left(x^2-x+8\right)+\left(10x^2+7\right)$ to $11x^2 - x + 15$.

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Introduction

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Simplifying algebraic expressions is a fundamental concept in mathematics, and it's essential to understand the process to excel in math. In our previous article, we provided a step-by-step guide on simplifying algebraic expressions. In this article, we'll address some frequently asked questions (FAQs) related to algebraic expression simplification.

Q&A Session

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Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or different powers of the same variable.

Example: $x^2$ and $10x^2$ are like terms because they both have the variable $x$ raised to the power of 2. On the other hand, $x^2$ and $y^2$ are unlike terms because they have different variables.

Q: How do I combine like terms?

A: To combine like terms, add their coefficients.

Example: To combine the like terms $x^2$ and $10x^2$, add their coefficients: $1 + 10 = 11$. The resulting term is $11x^2$.

Q: What is the simplified form of the expression $\left(x^2-x+8\right)+\left(10x^2+7\right)$?

A: The simplified form of the expression is $11x^2 - x + 15$.

Q: Can I simplify an expression with multiple variables?

A: Yes, you can simplify an expression with multiple variables by combining like terms.

Example: Simplify the expression $\left(x^2 + 2y^2\right) + \left(3x^2 + 4y^2\right)$. Combine the like terms: $x^2$ and $3x^2$ are like terms, and $2y^2$ and $4y^2$ are like terms. The resulting expression is $4x^2 + 6y^2$.

Q: How do I simplify an expression with parentheses?

A: To simplify an expression with parentheses, follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses.
2. Combine like terms.

Example: Simplify the expression $\left(2x^2 + 3\right) + \left(4x^2 - 2\right)$. Evaluate the expressions inside the parentheses: $2x^2 + 3$ and $4x^2 - 2$. Combine the like terms: $2x^2$ and $4x^2$ are like terms, and $3$ and $-2$ are like terms. The resulting expression is $6x^2 + 1$.

Q: Can I simplify an expression with fractions?

A: Yes, you can simplify an expression with fractions by combining like terms.

Example: Simplify the expression $\left(\frac{x^2}{2} + \frac{1}{3}\right) + \left(\frac{3x^2}{2} + \frac{2}{3}\right)$. Combine the like terms: $\frac{x^2}{2}$ and $\frac{3x^2}{2}$ are like terms, and $\frac{1}{3}$ and $\frac{2}{3}$ are like terms. The resulting expression is $\frac{4x^2}{2} + \frac{3}{3}$, which simplifies to $2x^2 + 1$.

Conclusion

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Simplifying algebraic expressions is an essential skill for any math enthusiast. By understanding the concepts of like and unlike terms, combining like terms, and following the order of operations, you can simplify complex expressions and arrive at a simplified form. We hope this Q&A guide has provided you with a better understanding of algebraic expression simplification.

Additional Resources

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For more information on simplifying algebraic expressions, check out the following resources:

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

Final Tips

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• Practice, practice, practice! The more you practice simplifying algebraic expressions, the more comfortable you'll become with the process.
• Use online resources, such as Khan Academy and Mathway, to help you understand and practice simplifying algebraic expressions.
• Don't be afraid to ask for help if you're struggling with a particular concept or problem.