Sharina Simplified The Expression $3(2x - 6 - X + 1)^2 - 2 + 4x$.In Step 1, She Simplified Within The Parentheses. In Step 2, She Expanded The Exponent.Sharina's Work:$[ \begin{tabular}{|l|c|} \hline \multicolumn{2}{|c|}{} \ \hline 1

Introduction

Sharina was given the expression $3(2x - 6 - x + 1)^2 - 2 + 4x$ and was asked to simplify it. In this article, we will go through her work step by step and see if she arrived at the correct solution.

Step 1: Simplifying within the Parentheses

Sharina started by simplifying the expression within the parentheses. She combined like terms and arrived at the following expression:

$$3(2x - x - 6 + 1)^2 - 2 + 4x$$

$$3(x - 5)^2 - 2 + 4x$$

Sharina's work is correct so far. She has simplified the expression within the parentheses and has arrived at a new expression.

Step 2: Expanding the Exponent

Sharina's next step was to expand the exponent. She used the formula $(a-b)^2 = a^2 - 2ab + b^2$ to expand the exponent. However, she made a mistake in her calculation.

$$3(x - 5)^2 - 2 + 4x$$

$$3(x^2 - 2x(5) + 5^2) - 2 + 4x$$

$$3(x^2 - 10x + 25) - 2 + 4x$$

Sharina's mistake was in the calculation of the exponent. She should have arrived at the following expression:

$$3(x^2 - 10x + 25) - 2 + 4x$$

$$3x^2 - 30x + 75 - 2 + 4x$$

Sharina's work is incorrect at this point. She made a mistake in expanding the exponent.

Correcting Sharina's Work

Let's go back to Sharina's work and correct her mistake. We will start by expanding the exponent correctly.

$$3(x - 5)^2 - 2 + 4x$$

$$3(x^2 - 2x(5) + 5^2) - 2 + 4x$$

$$3(x^2 - 10x + 25) - 2 + 4x$$

Now, let's simplify the expression further.

$$3x^2 - 30x + 75 - 2 + 4x$$

$$3x^2 - 26x + 73$$

Sharina's work is now correct. She has simplified the expression correctly.

Conclusion

Sharina's work was incorrect at first, but she was able to correct her mistake and arrive at the correct solution. The final simplified expression is $3x^2 - 26x + 73$. This expression is the result of simplifying the original expression $3(2x - 6 - x + 1)^2 - 2 + 4x$.

Discussion

Sharina's work is a great example of how to simplify an expression step by step. However, it is also a reminder that mistakes can happen, and it's essential to double-check our work to ensure that we arrive at the correct solution.

Key Takeaways

• Simplifying an expression involves breaking it down into smaller parts and simplifying each part separately.
• Expanding an exponent involves using the formula $(a-b)^2 = a^2 - 2ab + b^2$.
• It's essential to double-check our work to ensure that we arrive at the correct solution.

Final Answer

Introduction

In our previous article, we went through Sharina's work step by step and simplified the expression $3(2x - 6 - x + 1)^2 - 2 + 4x$. We also corrected her mistake and arrived at the correct solution. In this article, we will answer some frequently asked questions about simplifying expressions.

Q&A

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

A: The first step in simplifying an expression is to simplify the expression within the parentheses. This involves combining like terms and simplifying each part separately.

Q: How do I expand an exponent?

A: To expand an exponent, you can use the formula $(a-b)^2 = a^2 - 2ab + b^2$. This formula can be used to expand any exponent of the form $(a-b)^n$.

Q: What is the difference between simplifying an expression and expanding an exponent?

A: Simplifying an expression involves breaking it down into smaller parts and simplifying each part separately. Expanding an exponent involves using a formula to expand the exponent.

Q: How do I know if I have simplified an expression correctly?

A: To ensure that you have simplified an expression correctly, you should double-check your work. This involves going back through your steps and making sure 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:

• Not simplifying the expression within the parentheses
• Not expanding the exponent correctly
• Not double-checking your work

Q: How can I practice simplifying expressions?

A: You can practice simplifying expressions by working through example problems. You can also try simplifying expressions on your own and then checking your work to make sure that you have not made any mistakes.

Tips and Tricks

• Always simplify the expression within the parentheses first.
• Use the formula $(a-b)^2 = a^2 - 2ab + b^2$ to expand exponents.
• Double-check your work to ensure that you have not made any mistakes.
• Practice simplifying expressions regularly to improve your skills.

Conclusion

Simplifying expressions can be a challenging task, but with practice and patience, you can become proficient in simplifying expressions. Remember to always simplify the expression within the parentheses first, use the formula $(a-b)^2 = a^2 - 2ab + b^2$ to expand exponents, and double-check your work to ensure that you have not made any mistakes.

Final Answer

The final simplified expression is $3x^2 - 26x + 73$.