Select The Correct Answer.Simplify The Expression { -4x(6x-7)$}$.A. { -24x^2 + 28x$}$ B. { -24x^2 - 28x$}$ C. ${ 24x^2 + 28x\$} D. ${ 24x^2 - 28x\$}
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Introduction
Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we will focus on simplifying the expression {-4x(6x-7)$}$ and provide a step-by-step guide to help you arrive at the correct answer.
Understanding the Expression
The given expression is {-4x(6x-7)$}$. To simplify this expression, we need to apply the distributive property, which states that for any real numbers a, b, and c:
a(b + c) = ab + ac
Step 1: Apply the Distributive Property
Using the distributive property, we can rewrite the expression as:
{-4x(6x-7) = -4x(6x) + (-4x)(-7)$}$
Step 2: Simplify the Expression
Now, we can simplify the expression by multiplying the terms:
{-4x(6x) = -24x^2$}$
{(-4x)(-7) = 28x$}$
Step 3: Combine the Terms
Finally, we can combine the two terms to get the simplified expression:
{-24x^2 + 28x$}$
Conclusion
Based on the step-by-step guide provided above, we can conclude that the correct answer is:
A. {-24x^2 + 28x$}$
Discussion
The correct answer is A. {-24x^2 + 28x$}$. This is because the distributive property was applied correctly, and the terms were simplified and combined to get the final expression.
Common Mistakes
When simplifying algebraic expressions, it's essential to be careful with the signs and the order of operations. Some common mistakes include:
- Forgetting to apply the distributive property
- Misinterpreting the signs of the terms
- Not combining the terms correctly
Tips and Tricks
To simplify algebraic expressions efficiently, follow these tips and tricks:
- Always apply the distributive property when simplifying expressions with parentheses
- Be careful with the signs of the terms
- Combine the terms correctly to get the final expression
Final Answer
The final answer is A. {-24x^2 + 28x$}$.
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Introduction
In our previous article, we provided a step-by-step guide on how to simplify the expression {-4x(6x-7)$}$. In this article, we will provide a Q&A guide to help you understand the concepts and techniques involved in simplifying algebraic expressions.
Q&A
Q: What is the distributive property, and how is it used in simplifying expressions?
A: The distributive property is a mathematical concept that states that for any real numbers a, b, and c:
a(b + c) = ab + ac
This property is used to simplify expressions by distributing the terms inside the parentheses to the terms outside.
Q: How do I apply the distributive property to simplify expressions?
A: To apply the distributive property, you need to multiply each term inside the parentheses by the term outside the parentheses. For example, in the expression {-4x(6x-7)$}$, you would multiply -4x by 6x and -4x by -7.
Q: What is the difference between the expressions {-24x^2 + 28x$}$ and {-24x^2 - 28x$}$?
A: The expressions {-24x^2 + 28x$}$ and {-24x^2 - 28x$}$ differ only in the sign of the second term. The first expression has a positive sign, while the second expression has a negative sign.
Q: How do I determine the correct answer when simplifying expressions?
A: To determine the correct answer, you need to apply the distributive property, simplify the expression, and combine the terms correctly. You should also check your work to ensure that you have not made any mistakes.
Q: What are some common mistakes to avoid when simplifying expressions?
A: Some common mistakes to avoid when simplifying expressions include:
- Forgetting to apply the distributive property
- Misinterpreting the signs of the terms
- Not combining the terms correctly
Q: How can I practice simplifying expressions?
A: You can practice simplifying expressions by working through examples and exercises. You can also use online resources and practice tests to help you improve your skills.
Tips and Tricks
To simplify algebraic expressions efficiently, follow these tips and tricks:
- Always apply the distributive property when simplifying expressions with parentheses
- Be careful with the signs of the terms
- Combine the terms correctly to get the final expression
- Check your work to ensure that you have not made any mistakes
- Practice simplifying expressions regularly to improve your skills
Conclusion
Simplifying algebraic expressions is an essential skill in mathematics, and it's crucial to understand the concepts and techniques involved. By following the step-by-step guide and Q&A guide provided in this article, you can improve your skills and become more confident in simplifying expressions.
Final Answer
The final answer is A. {-24x^2 + 28x$}$.
Additional Resources
If you need additional help or resources to improve your skills, consider the following:
- Online resources: Websites such as Khan Academy, Mathway, and Wolfram Alpha offer interactive lessons, practice exercises, and calculators to help you learn and practice simplifying expressions.
- Practice tests: Practice tests and quizzes can help you assess your skills and identify areas where you need improvement.
- Textbooks and workbooks: Textbooks and workbooks can provide additional practice exercises and examples to help you improve your skills.
By following these resources and tips, you can become more confident in simplifying algebraic expressions and improve your overall math skills.