Which Expression Is Equivalent To \left(8x^3+8\right)-\left(x^3-2\right ]?A. 8 X 3 + 6 8x^3+6 8 X 3 + 6 B. 7 X 3 + 10 7x^3+10 7 X 3 + 10 C. 8 X 3 + 10 8x^3+10 8 X 3 + 10 D. 7 X 3 + 6 7x^3+6 7 X 3 + 6

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill for students and professionals alike. In this article, we will explore the process of simplifying algebraic expressions, with a focus on the given expression $\left(8x^3+8\right)-\left(x^3-2\right)$. We will break down the expression into manageable parts, apply the rules of algebra, and arrive at the simplified form.

Understanding the Expression

The given expression is a combination of two terms, each enclosed in parentheses. The first term is $8x^3+8$, and the second term is $x^3-2$. To simplify the expression, we need to apply the rules of algebra, specifically the distributive property and the order of operations.

Distributive Property

The distributive property states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. In the given expression, we can apply the distributive property to the second term, $x^3-2$, by multiplying each term inside the parentheses by $-1$.

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

Order of Operations

The order of operations is a set of rules that dictate the order in which we perform mathematical operations. The acronym PEMDAS is commonly used to remember the order of operations:

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.

In the given expression, we have already applied the distributive property, so we can now apply the order of operations.

8x^3+8 - x^3 + 2 = 8x^3 - x^3 + 8 + 2

Combining Like Terms

Like terms are terms that have the same variable and exponent. In the given expression, we have two like terms, $8x^3$ and $-x^3$. We can combine these terms by adding their coefficients.

8x^3 - x^3 = 7x^3

Now, we can rewrite the expression with the combined like terms.

7x^3 + 8 + 2

Final Simplification

The final step is to combine the constant terms, $8$ and $2$. We can do this by adding their values.

8 + 2 = 10

Now, we can rewrite the expression with the combined constant terms.

7x^3 + 10

Conclusion

In this article, we simplified the algebraic expression $\left(8x^3+8\right)-\left(x^3-2\right)$ by applying the distributive property and the order of operations. We combined like terms and arrived at the simplified form, $7x^3+10$. This expression is equivalent to the original expression, and it is the correct answer.

Answer

The correct answer is:

• B. $7x^3+10$

Final Thoughts

Introduction

In our previous article, we explored the process of simplifying algebraic expressions, with a focus on the given expression $\left(8x^3+8\right)-\left(x^3-2\right)$. We applied the distributive property and the order of operations to arrive at the simplified form, $7x^3+10$. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q: What is the distributive property?

A: The distributive property is a rule of algebra that states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. This means that we can distribute a single term to multiple terms inside parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, we need to multiply each term inside the parentheses by the single term outside the parentheses. For example, if we have the expression $a(b+c)$, we can apply the distributive property by multiplying $a$ by each term inside the parentheses: $ab + ac$.

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which we perform mathematical operations. The acronym PEMDAS is commonly used to remember the order of operations:

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: How do I combine like terms?

A: To combine like terms, we need to add or subtract the coefficients of the like terms. For example, if we have the expression $2x + 3x$, we can combine the like terms by adding their coefficients: $5x$.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, $2x$ and $3x$ are like terms because they have the same variable ($x$) and exponent (none).

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, we need to apply the distributive property and the order of operations. We can also combine like terms to simplify the expression.

Q: What is the final answer to the given expression?

A: The final answer to the given expression $\left(8x^3+8\right)-\left(x^3-2\right)$ is $7x^3+10$.

Q: Can I use a calculator to simplify algebraic expressions?

A: Yes, you can use a calculator to simplify algebraic expressions. However, it's always a good idea to check your work by hand to make sure you understand the process.

Q: How do I know if an expression is simplified?

A: An expression is simplified when there are no like terms that can be combined. In other words, the expression cannot be simplified further.

Conclusion

In this article, we answered some frequently asked questions about simplifying algebraic expressions. We hope that this guide will be helpful to anyone who needs to simplify algebraic expressions in the future. Remember to apply the distributive property and the order of operations, and combine like terms to simplify expressions.

Additional Resources

• Algebraic Expressions
• Distributive Property
• Order of Operations
• Like Terms

Final Thoughts

Simplifying algebraic expressions is an essential skill for students and professionals alike. By applying the rules of algebra, specifically the distributive property and the order of operations, we can simplify complex expressions and arrive at the correct answer. In this article, we demonstrated the process of simplifying an algebraic expression, and we hope that this guide will be helpful to anyone who needs to simplify algebraic expressions in the future.