Iliana Multiplied $3p - 7$ And $2p^2 - 3p - 4$. Her Work Is Shown In The Table.$ (3p - 7)(2p^2 - 3p - 4) $[ \begin{tabular}{|c|c|c|c|} \hline & 2 P 2 2p^2 2 P 2 & − 3 P -3p − 3 P & − 4 -4 − 4 \ \hline 3 P 3p 3 P & 6 P 3 6p^3 6 P 3 & − 9 P 2 -9p^2 − 9 P 2 & − 12 P -12p − 12 P
Introduction
In this article, we will delve into Iliana's multiplication problem, where she is tasked with multiplying two algebraic expressions: $3p - 7$ and $2p^2 - 3p - 4$. We will examine her work, identify any mistakes, and provide a step-by-step solution to the problem.
Iliana's Work
Iliana's work is shown in the table below:
\[ \begin{tabular}{|c|c|c|c|} \hline & $2p^2$ & $-3p$ & $-4$ \\ \hline $3p$ & $6p^3$ & $-9p^2$ & $-12p$ \end{tabular}
Analysis of Iliana's Work
At first glance, Iliana's work appears to be correct. However, upon closer inspection, we notice that she has only multiplied the first term of the first expression ($3p$) with the first term of the second expression ($2p^2$), resulting in $6p^3$. She has also multiplied the first term of the first expression ($3p$) with the second term of the second expression ($-3p$), resulting in $-9p^2$. Finally, she has multiplied the first term of the first expression ($3p$) with the third term of the second expression ($-4$), resulting in $-12p$.
However, Iliana has missed the terms that involve the constant term of the first expression ($-7$) and the variable terms of the second expression ($-3p$ and $-4$).
Step-by-Step Solution
To solve this problem, we need to multiply each term of the first expression ($3p - 7$) with each term of the second expression ($2p^2 - 3p - 4$).
Multiplying the First Term of the First Expression with Each Term of the Second Expression
The first term of the first expression is $3p$. We need to multiply this term with each term of the second expression.
- Multiplying $3p$ with $2p^2$: $3p \cdot 2p^2 = 6p^3$
- Multiplying $3p$ with $-3p$: $3p \cdot -3p = -9p^2$
- Multiplying $3p$ with $-4$: $3p \cdot -4 = -12p$
Multiplying the Second Term of the First Expression with Each Term of the Second Expression
The second term of the first expression is $-7$. We need to multiply this term with each term of the second expression.
- Multiplying $-7$ with $2p^2$: $-7 \cdot 2p^2 = -14p^2$
- Multiplying $-7$ with $-3p$: $-7 \cdot -3p = 21p$
- Multiplying $-7$ with $-4$: $-7 \cdot -4 = 28$
Combining the Terms
Now that we have multiplied each term of the first expression with each term of the second expression, we can combine the terms to get the final result.
Conclusion
In conclusion, Iliana's work was incomplete, and she missed several terms in her multiplication. By following the correct steps and multiplying each term of the first expression with each term of the second expression, we were able to arrive at the correct solution.
Key Takeaways
- When multiplying two algebraic expressions, make sure to multiply each term of one expression with each term of the other expression.
- Don't forget to include the constant terms and variable terms in your multiplication.
- Combine the terms carefully to get the final result.
Introduction
In our previous article, we delved into Iliana's multiplication problem, where she was tasked with multiplying two algebraic expressions: $3p - 7$ and $2p^2 - 3p - 4$. We examined her work, identified any mistakes, and provided a step-by-step solution to the problem.
Q&A Session
In this article, we will address some common questions related to Iliana's multiplication problem and provide additional insights to help you better understand the concept.
Q: What is the correct solution to Iliana's multiplication problem?
A: The correct solution to Iliana's multiplication problem is:
Q: Why did Iliana miss some terms in her multiplication?
A: Iliana missed some terms in her multiplication because she only multiplied the first term of the first expression ($3p$) with the first term of the second expression ($2p^2$), resulting in $6p^3$. She also multiplied the first term of the first expression ($3p$) with the second term of the second expression ($-3p$), resulting in $-9p^2$. Finally, she multiplied the first term of the first expression ($3p$) with the third term of the second expression ($-4$), resulting in $-12p$. However, she missed the terms that involve the constant term of the first expression ($-7$) and the variable terms of the second expression ($-3p$ and $-4$).
Q: How can I avoid making the same mistake as Iliana?
A: To avoid making the same mistake as Iliana, make sure to multiply each term of one expression with each term of the other expression. Don't forget to include the constant terms and variable terms in your multiplication. Combine the terms carefully to get the final result.
Q: What are some common mistakes to watch out for when multiplying algebraic expressions?
A: Some common mistakes to watch out for when multiplying algebraic expressions include:
- Forgetting to multiply each term of one expression with each term of the other expression
- Missing the constant terms and variable terms in your multiplication
- Not combining the terms carefully to get the final result
- Not using the correct order of operations (PEMDAS)
Q: How can I practice multiplying algebraic expressions?
A: To practice multiplying algebraic expressions, try the following:
- Start with simple expressions and gradually move on to more complex ones
- Use online resources and practice problems to help you build your skills
- Work with a partner or tutor to get feedback and guidance
- Review and practice regularly to reinforce your understanding of the concept
Conclusion
In conclusion, Iliana's multiplication problem was a great opportunity to review and practice multiplying algebraic expressions. By following the correct steps and avoiding common mistakes, you can ensure that your multiplication problems are accurate and complete.
Key Takeaways
- When multiplying two algebraic expressions, make sure to multiply each term of one expression with each term of the other expression.
- Don't forget to include the constant terms and variable terms in your multiplication.
- Combine the terms carefully to get the final result.
- Practice regularly to reinforce your understanding of the concept.
By following these key takeaways, you can become more confident and proficient in multiplying algebraic expressions.