Subtract: \left(10x^8 - 8\right) - \left(-15x^8\right ]Your Answer Should Be In Simplest Terms. Enter The Correct Answer.

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Understanding the Problem

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When dealing with algebraic expressions, it's essential to understand the rules of simplification. In this article, we'll focus on subtracting one expression from another, specifically the given problem: $\left(10x^8 - 8\right) - \left(-15x^8\right)$. Our goal is to simplify this expression and present the answer in its simplest terms.

The Rules of Simplification

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Before we dive into the problem, let's review the basic rules of simplification:

• When subtracting a negative number, we add the absolute value of that number.
• When subtracting a positive number, we subtract the number itself.
• We can combine like terms by adding or subtracting their coefficients.

Applying the Rules to the Problem

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Now that we've reviewed the rules, let's apply them to the given problem:

$\left(10x^8 - 8\right) - \left(-15x^8\right)$

To simplify this expression, we'll follow the order of operations (PEMDAS):

1. Parentheses: We'll start by evaluating the expressions inside the parentheses.
2. Exponents: We'll then evaluate any exponents (in this case, none).
3. Multiplication and Division: We'll perform any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, we'll perform any addition and subtraction operations from left to right.

Step 1: Evaluate the Expressions Inside the Parentheses

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Let's start by evaluating the expressions inside the parentheses:

$\left(10x^8 - 8\right) = 10x^8 - 8$

$\left(-15x^8\right) = -15x^8$

Step 2: Rewrite the Expression with the Evaluated Parentheses

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Now that we've evaluated the expressions inside the parentheses, we can rewrite the original expression:

$10x^8 - 8 - (-15x^8)$

Step 3: Apply the Rule of Subtracting a Negative Number

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According to the rules of simplification, when subtracting a negative number, we add the absolute value of that number. In this case, we'll add $15x^8$ to the expression:

$10x^8 - 8 + 15x^8$

Step 4: Combine Like Terms

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Now that we've applied the rule of subtracting a negative number, we can combine like terms by adding their coefficients:

$(10x^8 + 15x^8) - 8$

Step 5: Simplify the Expression

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Finally, we can simplify the expression by combining the like terms:

$25x^8 - 8$

Conclusion

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In this article, we've simplified the given algebraic expression $\left(10x^8 - 8\right) - \left(-15x^8\right)$ using the rules of simplification. By following the order of operations and applying the rules of subtracting a negative number and combining like terms, we arrived at the simplified expression: $25x^8 - 8$. This expression is in its simplest terms, and we've provided a step-by-step guide to help readers understand the process.

Frequently Asked Questions

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Q: What is the simplified expression for $\left(10x^8 - 8\right) - \left(-15x^8\right)$?

A: The simplified expression is $25x^8 - 8$.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, follow the order of operations (PEMDAS) and apply the rules of simplification, including subtracting a negative number and combining like terms.

Q: What are like terms in algebra?

A: Like terms are terms that have the same variable(s) raised to the same power. In the expression $10x^8 + 15x^8$, $10x^8$ and $15x^8$ are like terms because they both have the variable $x$ raised to the power of 8.

Additional Resources

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

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

By following the steps outlined in this article and practicing with additional resources, you'll become proficient in simplifying algebraic expressions and solving problems like the one presented.

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Introduction

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Simplifying algebraic expressions is a crucial skill in mathematics, and it can be a bit challenging for beginners. In this article, we'll provide a comprehensive Q&A guide to help you understand the concepts and techniques involved in simplifying algebraic expressions.

Q&A: Simplifying Algebraic Expressions

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Q: What is an algebraic expression?

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

Q: What are the rules of simplification?

A: The rules of simplification are:

• When subtracting a negative number, we add the absolute value of that number.
• When subtracting a positive number, we subtract the number itself.
• We can combine like terms by adding or subtracting their coefficients.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, follow the order of operations (PEMDAS) and apply the rules of simplification, including subtracting a negative number and combining like terms.

Q: What is the order of operations (PEMDAS)?

A: The order of operations is a set of rules that tells us which operations to perform first when simplifying an algebraic expression. The acronym PEMDAS stands for:

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponents (such as squaring or cubing) next.
• Multiplication and Division: Perform any multiplication and division operations from left to right.
• Addition and Subtraction: Finally, perform any addition and subtraction operations from left to right.

Q: What are like terms in algebra?

A: Like terms are terms that have the same variable(s) raised to the same power. In the expression $10x^8 + 15x^8$, $10x^8$ and $15x^8$ are like terms because they both have the variable $x$ raised to the power of 8.

Q: How do I combine like terms?

A: To combine like terms, add or subtract their coefficients. For example, in the expression $10x^8 + 15x^8$, we can combine the like terms by adding their coefficients: $10 + 15 = 25$. The resulting expression is $25x^8$.

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. In the expression $2x + 3$, $x$ is a variable and $3$ is a constant.

Q: How do I simplify an expression with multiple variables?

A: To simplify an expression with multiple variables, follow the same rules as before. However, be careful to combine like terms that have the same variables raised to the same power.

Q: What are some common algebraic expressions?

A: Some common algebraic expressions include:

• Linear expressions: $ax + b$
• Quadratic expressions: $ax^2 + bx + c$
• Polynomial expressions: $a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$

Conclusion

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Simplifying algebraic expressions is an essential skill in mathematics, and it can be a bit challenging for beginners. However, with practice and patience, you'll become proficient in simplifying algebraic expressions and solving problems like the ones presented in this article. Remember to follow the order of operations (PEMDAS) and apply the rules of simplification, including subtracting a negative number and combining like terms.

Additional Resources

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

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

By following the steps outlined in this article and practicing with additional resources, you'll become proficient in simplifying algebraic expressions and solving problems like the one presented.