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

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and evaluating them is a crucial skill for students to master. In this article, we will focus on evaluating the expression x6−x4y\frac{x^6-x}{4y} when x=−4x=-4 and y=4y=4. We will break down the problem step by step, using algebraic techniques to simplify the expression and arrive at the correct answer.

Understanding the Expression

The given expression is x6−x4y\frac{x^6-x}{4y}. This expression involves exponentiation, subtraction, and division. To evaluate it, we need to follow the order of operations (PEMDAS):

  1. Parentheses: None
  2. Exponents: Evaluate the exponentiation
  3. Multiplication and Division: Evaluate from left to right
  4. Addition and Subtraction: Evaluate from left to right

Step 1: Evaluate the Exponentiation

The expression involves the term x6x^6. To evaluate this, we need to raise xx to the power of 6.

x6=(−4)6x^6 = (-4)^6

Using the property of negative exponents, we can rewrite this as:

x6=(−4)6=46x^6 = (-4)^6 = 4^6

Now, we can evaluate the exponentiation:

46=40964^6 = 4096

Step 2: Simplify the Expression

Now that we have evaluated the exponentiation, we can simplify the expression:

x6−x4y=4096−(−4)4(4)\frac{x^6-x}{4y} = \frac{4096-(-4)}{4(4)}

Using the property of negative numbers, we can rewrite the subtraction as:

4096+44(4)\frac{4096+4}{4(4)}

Now, we can simplify the expression further:

410016\frac{4100}{16}

Step 3: Simplify the Fraction

The expression 410016\frac{4100}{16} can be simplified further by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4.

410016=10254\frac{4100}{16} = \frac{1025}{4}

Conclusion

In conclusion, the correct answer is 10254\frac{1025}{4}. This is the result of evaluating the expression x6−x4y\frac{x^6-x}{4y} when x=−4x=-4 and y=4y=4.

Answer Options

The answer options are:

A. 10234\frac{1023}{4} B. −10234-\frac{1023}{4} C. 163854\frac{16385}{4} D. 10254\frac{1025}{4}

The correct answer is D. 10254\frac{1025}{4}.

Discussion

Evaluating algebraic expressions is a crucial skill for students to master. In this article, we have broken down the problem step by step, using algebraic techniques to simplify the expression and arrive at the correct answer. The correct answer is 10254\frac{1025}{4}.

Tips and Tricks

  • When evaluating algebraic expressions, always follow the order of operations (PEMDAS).
  • Use algebraic techniques to simplify the expression and arrive at the correct answer.
  • Check your work by plugging in the values of the variables and evaluating the expression.

Practice Problems

  • Evaluate the expression x3−x3y\frac{x^3-x}{3y} when x=2x=2 and y=3y=3.
  • Evaluate the expression x2−x2y\frac{x^2-x}{2y} when x=−2x=-2 and y=2y=2.

Conclusion

Introduction

In our previous article, we discussed how to evaluate the expression x6−x4y\frac{x^6-x}{4y} when x=−4x=-4 and y=4y=4. We broke down the problem step by step, using algebraic techniques to simplify the expression and arrive at the correct answer. In this article, we will provide a Q&A guide to help you evaluate algebraic expressions.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The order of operations is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate 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 evaluate an exponential expression?

A: To evaluate an exponential expression, you need to raise the base number to the power of the exponent. For example, to evaluate x3x^3, you need to raise xx to the power of 3.

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.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify 1218\frac{12}{18}, you need to divide both 12 and 18 by their GCD, which is 6.

Q: What is the greatest common divisor (GCD)?

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

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

A: To evaluate an expression with multiple variables, you need to substitute the values of the variables into the expression and then evaluate it.

Q: What is the difference between a linear expression and a quadratic expression?

A: A linear expression is an expression with one variable and a degree of 1. A quadratic expression is an expression with one variable and a degree of 2.

Q: How do I evaluate an expression with absolute value?

A: To evaluate an expression with absolute value, you need to consider both the positive and negative values of the expression.

Q: What is the difference between a rational expression and an irrational expression?

A: A rational expression is an expression that can be written as a fraction of two integers. An irrational expression is an expression that cannot be written as a fraction of two integers.

Q: How do I evaluate an expression with a negative exponent?

A: To evaluate an expression with a negative exponent, you need to rewrite the expression with a positive exponent and then take the reciprocal of the expression.

Conclusion

In conclusion, evaluating algebraic expressions is a crucial skill for students to master. By following the order of operations and using algebraic techniques, we can simplify the expression and arrive at the correct answer. We hope this Q&A guide has helped you evaluate algebraic expressions with confidence.

Practice Problems

  • Evaluate the expression x2−x2y\frac{x^2-x}{2y} when x=3x=3 and y=2y=2.
  • Evaluate the expression x3−x3y\frac{x^3-x}{3y} when x=−2x=-2 and y=3y=3.

Tips and Tricks

  • Always follow the order of operations (PEMDAS).
  • Use algebraic techniques to simplify the expression and arrive at the correct answer.
  • Check your work by plugging in the values of the variables and evaluating the expression.

Resources

  • Khan Academy: Algebra
  • Mathway: Algebra Calculator
  • Wolfram Alpha: Algebra Solver