Select The Correct Answer.Evaluate The Following Expression When $x = -4$ And $y = 4$. X 6 − X 4 Y \frac{x^6 - X}{4y} 4 Y X 6 − X ​ A. 1 , 023 4 \frac{1,023}{4} 4 1 , 023 ​ B. 1 , 025 4 \frac{1,025}{4} 4 1 , 025 ​ C. 1 , 023 4 \frac{1,023}{4} 4 1 , 023 ​ D. 16 , 385 4 \frac{16,385}{4} 4 16 , 385 ​

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Introduction

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In mathematics, evaluating expressions is a crucial skill that helps us solve problems and make informed decisions. In this article, we will focus on evaluating the expression $\frac{x^6 - x}{4y}$ when $x = -4$ and $y = 4$. We will break down the problem step by step, using mathematical concepts and formulas to arrive at the correct answer.

Understanding the Expression

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The given expression is $\frac{x^6 - x}{4y}$. To evaluate this expression, we need to substitute the values of $x$ and $y$ into the expression and simplify it.

Substituting Values

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We are given that $x = -4$ and $y = 4$. We will substitute these values into the expression:

$$\frac{x^6 - x}{4y} = \frac{(-4)^6 - (-4)}{4(4)}$$

Simplifying the Expression

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Now, let's simplify the expression:

$$\frac{(-4)^6 - (-4)}{4(4)} = \frac{4096 + 4}{16}$$

$$= \frac{4100}{16}$$

Further Simplification

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We can further simplify the expression by dividing both the numerator and the denominator by their greatest common divisor, which is 4:

$$\frac{4100}{16} = \frac{1025}{4}$$

Evaluating the Expression

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Now that we have simplified the expression, we can evaluate it by substituting the values of $x$ and $y$:

$$\frac{x^6 - x}{4y} = \frac{(-4)^6 - (-4)}{4(4)} = \frac{4100}{16} = \frac{1025}{4}$$

Conclusion

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In conclusion, the correct answer is $\frac{1025}{4}$. This is the result of evaluating the expression $\frac{x^6 - x}{4y}$ when $x = -4$ and $y = 4$.

Final Answer

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The final answer is $\boxed{\frac{1025}{4}}$.

Discussion

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The expression $\frac{x^6 - x}{4y}$ is a simple algebraic expression that can be evaluated using basic mathematical concepts and formulas. The key to solving this problem is to substitute the values of $x$ and $y$ into the expression and simplify it step by step.

Common Mistakes

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When evaluating expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

• Not substituting the values of $x$ and $y$ into the expression
• Not simplifying the expression step by step
• Not checking for errors in the calculation

Tips and Tricks

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Here are some tips and tricks to help you evaluate expressions like this:

• Always read the problem carefully and understand what is being asked
• Substitute the values of $x$ and $y$ into the expression
• Simplify the expression step by step
• Check for errors in the calculation

Practice Problems

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If you want to practice evaluating expressions like this, here are some practice problems:

• Evaluate the expression $\frac{x^3 - x}{3y}$ when $x = 2$ and $y = 3$.
• Evaluate the expression $\frac{x^4 - x}{2y}$ when $x = -2$ and $y = 2$.

Conclusion

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In conclusion, evaluating expressions is a crucial skill that helps us solve problems and make informed decisions. By following the steps outlined in this article, you can evaluate expressions like $\frac{x^6 - x}{4y}$ when $x = -4$ and $y = 4$. Remember to substitute the values of $x$ and $y$ into the expression, simplify it step by step, and check for errors in the calculation.

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Introduction

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In our previous article, we discussed how to evaluate the expression $\frac{x^6 - x}{4y}$ when $x = -4$ and $y = 4$. In this article, we will provide a Q&A guide to help you understand the concepts and formulas involved in evaluating expressions.

Q&A

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Q: What is the first step in evaluating an expression?

A: The first step in evaluating an expression is to substitute the values of the variables into the expression.

Q: How do I simplify an expression?

A: To simplify an expression, you need to follow the order of operations (PEMDAS):

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 greatest common divisor (GCD)?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: There are several ways to find the GCD of two numbers. One way is to list the factors of each number and find the greatest common factor.

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

A: A variable is a symbol that represents a value that can change, while a constant is a value that does not change.

Q: How do I evaluate an expression with variables and constants?

A: To evaluate an expression with variables and constants, you need to substitute the values of the variables into the expression and simplify it using the order of operations.

Q: What is the final answer to the expression $\frac{x^6 - x}{4y}$ when $x = -4$ and $y = 4$?

A: The final answer to the expression $\frac{x^6 - x}{4y}$ when $x = -4$ and $y = 4$ is $\frac{1025}{4}$.

Common Mistakes

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

A: Some common mistakes to avoid when evaluating expressions include:

• Not substituting the values of the variables into the expression
• Not simplifying the expression step by step
• Not checking for errors in the calculation

Tips and Tricks

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Q: What are some tips and tricks to help me evaluate expressions?

A: Some tips and tricks to help you evaluate expressions include:

• Always read the problem carefully and understand what is being asked
• Substitute the values of the variables into the expression
• Simplify the expression step by step
• Check for errors in the calculation

Practice Problems

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Q: What are some practice problems to help me evaluate expressions?

A: Some practice problems to help you evaluate expressions include:

• Evaluate the expression $\frac{x^3 - x}{3y}$ when $x = 2$ and $y = 3$.
• Evaluate the expression $\frac{x^4 - x}{2y}$ when $x = -2$ and $y = 2$.

Conclusion

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In conclusion, evaluating expressions is a crucial skill that helps us solve problems and make informed decisions. By following the steps outlined in this article, you can evaluate expressions like $\frac{x^6 - x}{4y}$ when $x = -4$ and $y = 4$. Remember to substitute the values of the variables into the expression, simplify it step by step, and check for errors in the calculation.

Final Answer

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The final answer is $\boxed{\frac{1025}{4}}$.