Which Choice Is Equivalent To The Expression Below?${5 \sqrt{7} - 4x \sqrt{7} - X \sqrt{7}}$A. ${5 \sqrt{7} - 5x \sqrt{7}}$B. 0C. ${-x^2}$D. ${-2x \sqrt{7}}$

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Understanding the Problem

When dealing with algebraic expressions, it's essential to simplify them to make calculations easier and more manageable. In this article, we'll focus on simplifying an expression involving square roots and variables. We'll explore the given expression and determine which choice is equivalent to it.

The Given Expression

The given expression is:

57−4x7−x7{5 \sqrt{7} - 4x \sqrt{7} - x \sqrt{7}}

This expression involves a square root term, 7\sqrt{7}, multiplied by constants and variables. Our goal is to simplify this expression and identify the equivalent choice from the given options.

Simplifying the Expression

To simplify the expression, we can start by factoring out the common term, 7\sqrt{7}. This will help us combine like terms and simplify the expression.

import sympy as sp

x = sp.symbols('x')



expr = 5sp.sqrt(7) - 4xsp.sqrt(7) - xsp.sqrt(7)



simplified_expr = sp.simplify(expr)

By factoring out the common term, 7\sqrt{7}, we get:

57−x7(4+1){5 \sqrt{7} - x \sqrt{7} (4 + 1)}

Now, we can simplify the expression further by combining like terms:

57−5x7{5 \sqrt{7} - 5x \sqrt{7}}

Comparing with the Options

Now that we have simplified the expression, let's compare it with the given options:

A. ${5 \sqrt{7} - 5x \sqrt{7}}$

B. 0

C. ${-x^2}$

D. ${-2x \sqrt{7}}$

Based on our simplified expression, we can see that option A is equivalent to the given expression.

Conclusion

In this article, we simplified an algebraic expression involving square roots and variables. We factored out the common term, 7\sqrt{7}, and combined like terms to simplify the expression. By comparing the simplified expression with the given options, we determined that option A is equivalent to the given expression.

Key Takeaways

  • When dealing with algebraic expressions, it's essential to simplify them to make calculations easier and more manageable.
  • Factoring out common terms can help combine like terms and simplify the expression.
  • By simplifying the expression, we can identify equivalent choices from the given options.

Further Reading

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 Answer

The final answer is:

Introduction

In our previous article, we explored the process of simplifying algebraic expressions involving square roots and variables. We factored out common terms and combined like terms to simplify the expression. In this article, we'll answer some frequently asked questions (FAQs) related to simplifying algebraic expressions.

Q&A

Q: What is the first step in simplifying an algebraic expression?

A: The first step in simplifying an algebraic expression is to identify the common terms and factor them out. This will help you combine like terms and simplify the expression.

Q: How do I identify common terms in an algebraic expression?

A: To identify common terms, look for terms that have the same variable or constant factor. For example, in the expression 3x+2x3x + 2x, the common term is xx.

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

A: Like terms are terms that have the same variable or constant factor, while unlike terms are terms that have different variables or constant factors. For example, in the expression 3x+2y3x + 2y, 3x3x and 2y2y are unlike terms because they have different variables.

Q: How do I combine like terms in an algebraic expression?

A: To combine like terms, add or subtract the coefficients of the like terms. For example, in the expression 3x+2x3x + 2x, the coefficients are 33 and 22. Adding them together gives 5x5x.

Q: What is the importance of simplifying algebraic expressions?

A: Simplifying algebraic expressions is important because it makes calculations easier and more manageable. It also helps to identify equivalent choices from the given options.

Q: Can I simplify an algebraic expression by rearranging the terms?

A: Yes, you can simplify an algebraic expression by rearranging the terms. However, this should be done carefully to avoid changing the value of the expression.

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

A: An algebraic expression is already simplified if there are no like terms that can be combined. You can also check if the expression is in its simplest form by factoring out common terms and combining like terms.

Q: Can I use a calculator to simplify an algebraic expression?

A: Yes, you can use a calculator to simplify an algebraic expression. However, it's always a good idea to check the result manually to ensure that it's correct.

Conclusion

In this article, we answered some frequently asked questions related to simplifying algebraic expressions. We covered topics such as identifying common terms, combining like terms, and the importance of simplifying algebraic expressions. By following these tips and techniques, you'll be able to simplify algebraic expressions with ease.

Key Takeaways

  • Identifying common terms is the first step in simplifying an algebraic expression.
  • Combining like terms involves adding or subtracting the coefficients of the like terms.
  • Simplifying algebraic expressions makes calculations easier and more manageable.
  • You can use a calculator to simplify an algebraic expression, but it's always a good idea to check the result manually.

Further Reading

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 Answer

The final answer is: There is no final answer, as this article is a Q&A guide.