Factorize $rt - Ru$.A. $y(r - Ru)$ B. \$r(u - T)$[/tex\] C. $r(t - U)$ D. $t(r - U)$
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Introduction
Factorization is a fundamental concept in algebra that involves expressing an algebraic expression as a product of simpler expressions. In this article, we will focus on factorizing the expression $rt - ru$, where $r$, $t$, and $u$ are variables. We will explore different methods of factorization and provide step-by-step solutions to help you understand the concept better.
Understanding the Expression
The given expression is $rt - ru$. To factorize this expression, we need to identify the common factors among the terms. In this case, we can see that both terms have a common factor of $r$.
Method 1: Factoring out $r$
We can factor out $r$ from both terms using the distributive property. The distributive property states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. In this case, we can rewrite the expression as:
This is the factored form of the expression, where $r$ is the common factor.
Method 2: Factoring out $t - u$
Alternatively, we can factor out $t - u$ from both terms. This method involves recognizing that $t - u$ is a common factor of the two terms.
This is another valid factorization of the expression, where $t - u$ is the common factor.
Comparison of Methods
Both methods of factorization are valid, and the choice of method depends on the context and the specific problem. In some cases, factoring out $r$ may be more convenient, while in other cases, factoring out $t - u$ may be more suitable.
Conclusion
In conclusion, factorizing the expression $rt - ru$ involves identifying the common factors among the terms and using the distributive property to rewrite the expression in a factored form. We have explored two methods of factorization, factoring out $r$ and factoring out $t - u$, and demonstrated that both methods are valid. By understanding the concept of factorization and applying it to different expressions, you can develop a deeper appreciation for algebra and improve your problem-solving skills.
Frequently Asked Questions
Q: What is factorization in algebra?
A: Factorization is a process of expressing an algebraic expression as a product of simpler expressions.
Q: How do I factorize an expression?
A: To factorize an expression, identify the common factors among the terms and use the distributive property to rewrite the expression in a factored form.
Q: What are the common factors of the expression $rt - ru$?
A: The common factors of the expression $rt - ru$ are $r$ and $t - u$.
Q: Can I factor out $t - u$ from both terms?
A: Yes, you can factor out $t - u$ from both terms using the distributive property.
Q: What is the factored form of the expression $rt - ru$?
A: The factored form of the expression $rt - ru$ is $r(t - u)$.
Final Answer
The final answer is:
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Introduction
In our previous article, we explored the concept of factorizing the expression $rt - ru$ and provided step-by-step solutions to help you understand the concept better. In this article, we will focus on providing a comprehensive guide to Q&A related to factorizing the expression $rt - ru$.
Q&A: Factorizing $rt - ru$
Q: What is the main concept of factorizing $rt - ru$?
A: The main concept of factorizing $rt - ru$ involves identifying the common factors among the terms and using the distributive property to rewrite the expression in a factored form.
Q: How do I identify the common factors of $rt - ru$?
A: To identify the common factors of $rt - ru$, look for the terms that have a common factor. In this case, both terms have a common factor of $r$.
Q: Can I factor out $t - u$ from both terms?
A: Yes, you can factor out $t - u$ from both terms using the distributive property.
Q: What is the factored form of the expression $rt - ru$?
A: The factored form of the expression $rt - ru$ is $r(t - u)$.
Q: Can I factor out $r$ from both terms?
A: Yes, you can factor out $r$ from both terms using the distributive property.
Q: What is the difference between factoring out $r$ and factoring out $t - u$?
A: Factoring out $r$ involves recognizing that $r$ is a common factor of both terms, while factoring out $t - u$ involves recognizing that $t - u$ is a common factor of both terms.
Q: Can I factor out $t$ from both terms?
A: No, you cannot factor out $t$ from both terms because $t$ is not a common factor of both terms.
Q: Can I factor out $u$ from both terms?
A: No, you cannot factor out $u$ from both terms because $u$ is not a common factor of both terms.
Advanced Q&A
Q: What is the relationship between the distributive property and factorization?
A: The distributive property is a fundamental concept in algebra that allows us to rewrite an expression in a factored form. Factorization involves using the distributive property to identify the common factors among the terms.
Q: Can I factorize an expression with multiple variables?
A: Yes, you can factorize an expression with multiple variables by identifying the common factors among the terms and using the distributive property to rewrite the expression in a factored form.
Q: What is the importance of factorization in algebra?
A: Factorization is an essential concept in algebra that allows us to simplify complex expressions and solve equations. It is a powerful tool for problem-solving and is used extensively in various fields, including mathematics, science, and engineering.
Conclusion
In conclusion, factorizing the expression $rt - ru$ involves identifying the common factors among the terms and using the distributive property to rewrite the expression in a factored form. We have provided a comprehensive guide to Q&A related to factorizing the expression $rt - ru$, including advanced questions and answers. By understanding the concept of factorization and applying it to different expressions, you can develop a deeper appreciation for algebra and improve your problem-solving skills.
Frequently Asked Questions
Q: What is factorization in algebra?
A: Factorization is a process of expressing an algebraic expression as a product of simpler expressions.
Q: How do I factorize an expression?
A: To factorize an expression, identify the common factors among the terms and use the distributive property to rewrite the expression in a factored form.
Q: What are the common factors of the expression $rt - ru$?
A: The common factors of the expression $rt - ru$ are $r$ and $t - u$.
Q: Can I factor out $t - u$ from both terms?
A: Yes, you can factor out $t - u$ from both terms using the distributive property.
Q: What is the factored form of the expression $rt - ru$?
A: The factored form of the expression $rt - ru$ is $r(t - u)$.
Final Answer
The final answer is: