Comparing with the Original Expression

Oct 13, 2025 by pynkocean.com 87 views

Introduction

Algebraic expressions are a fundamental concept in mathematics, and understanding how to manipulate and simplify them is crucial for solving equations and inequalities. However, errors can occur when expanding or simplifying expressions, leading to incorrect solutions. In this article, we will analyze a given expression and identify the errors made by Daniel.

The Expression

Daniel expanded the expression as shown:

-2\left(-8x - 4y + \frac{3}{4}\right) = 10x - 8y - 1 \frac{1}{4}

Step 1: Distributing the Negative 2

To evaluate the expression, we need to distribute the negative 2 to each term inside the parentheses. This means multiplying each term by -2.

-2\left(-8x - 4y + \frac{3}{4}\right) = -2(-8x) - 2(-4y) - 2\left(\frac{3}{4}\right)

Step 2: Simplifying the Expression

Now, we simplify each term by multiplying the negative 2 by each term.

-2(-8x) = 16x

-2(-4y) = 8y

-2\left(\frac{3}{4}\right) = -\frac{3}{2}

Step 3: Combining Like Terms

We combine the like terms to simplify the expression further.

16x + 8y - \frac{3}{2}

Comparing with the Original Expression

Now, we compare the simplified expression with the original expression to identify any errors.

16x + 8y - \frac{3}{2} = 10x - 8y - 1 \frac{1}{4}

Error Analysis

Based on the comparison, we can identify the errors made by Daniel.

The first term should be negative, not positive. The correct term should be $-16x$ .
The second term should be negative, not positive. The correct term should be $-8y$ .
The third term should be positive, not negative. The correct term should be $\frac{3}{2}$ .

Conclusion

In conclusion, Daniel made three errors when expanding the expression. The correct expansion of the expression is $-16x - 8y + \frac{3}{2}$ . This highlights the importance of carefully distributing and simplifying algebraic expressions to avoid errors.

Recommendations

To avoid similar errors, it is essential to:

Carefully distribute coefficients to each term inside the parentheses.
Simplify each term by multiplying the coefficient by each term.
Combine like terms to simplify the expression further.
Compare the simplified expression with the original expression to identify any errors.

By following these steps and recommendations, you can ensure accurate and reliable results when working with algebraic expressions.

Frequently Asked Questions

Q: What is the correct expansion of the expression?

A: The correct expansion of the expression is $-16x - 8y + \frac{3}{2}$ .

Q: What are the errors made by Daniel?

A: The errors made by Daniel are:

The first term should be negative, not positive.
The second term should be negative, not positive.
The third term should be positive, not negative.

Q: How can I avoid similar errors?

Q&A: Common Questions and Answers

Q: What is the most common mistake when expanding algebraic expressions? A: The most common mistake is not distributing the coefficient to each term inside the parentheses.

Q: How can I ensure that I am distributing the coefficient correctly? A: To ensure that you are distributing the coefficient correctly, multiply the coefficient by each term inside the parentheses and simplify each term.

Q: What is the difference between a like term and a unlike term? A: A like term is a term that has the same variable(s) raised to the same power, while a unlike term is a term that has different variable(s) raised to different powers.

Q: How can I combine like terms? A: To combine like terms, add or subtract the coefficients of the like terms and keep the variable(s) the same.

Q: What is the importance of simplifying algebraic expressions? A: Simplifying algebraic expressions is important because it helps to make the expression easier to work with and can help to identify errors.

Q: How can I identify errors in algebraic expressions? A: To identify errors in algebraic expressions, compare the simplified expression with the original expression and look for any discrepancies.

Q: What are some common errors to watch out for when working with algebraic expressions? A: Some common errors to watch out for when working with algebraic expressions include:

Not distributing the coefficient correctly
Not simplifying the expression correctly
Not combining like terms correctly
Not identifying errors in the expression

Q: How can I practice evaluating errors in algebraic expressions? A: To practice evaluating errors in algebraic expressions, try working through examples and exercises that involve expanding and simplifying algebraic expressions. You can also try creating your own examples and exercises to test your skills.

Q: What are some resources available for learning more about algebraic expressions? A: Some resources available for learning more about algebraic expressions include:

Textbooks and online resources that provide step-by-step instructions and examples
Online tutorials and videos that provide visual explanations and demonstrations
Practice problems and exercises that allow you to test your skills and knowledge

Conclusion

In conclusion, evaluating errors in algebraic expressions is an important skill that requires attention to detail and a thorough understanding of algebraic concepts. By following the steps outlined in this article and practicing regularly, you can develop your skills and become more confident in your ability to evaluate errors in algebraic expressions.

Additional Resources

Frequently Asked Questions

Q: What is the best way to learn algebraic expressions?

A: The best way to learn algebraic expressions is to practice regularly and work through examples and exercises.

Q: How can I improve my skills in evaluating errors in algebraic expressions?

A: To improve your skills in evaluating errors in algebraic expressions, try working through examples and exercises that involve expanding and simplifying algebraic expressions.

Q: What are some common mistakes to watch out for when working with algebraic expressions?

A: Some common mistakes to watch out for when working with algebraic expressions include not distributing the coefficient correctly, not simplifying the expression correctly, not combining like terms correctly, and not identifying errors in the expression.