Which Of The Following Illustrates How To Find The Difference Of $12a^2b$ And $-5a^2b$?A. $ ( 12 − 5 ) A 2 B (12-5)a^2b ( 12 − 5 ) A 2 B [/tex]B. $(12+5)a 4b 2$C. $(12+5)a^2b$D. $ ( 12 − 5 ) A 4 B 2 (12-5)a^4b^2 ( 12 − 5 ) A 4 B 2 [/tex]
Introduction to Algebraic Expressions
Algebraic expressions are a fundamental concept in mathematics, and they play a crucial role in solving various mathematical problems. An algebraic expression is a combination of variables, constants, and mathematical operations. In this article, we will focus on understanding how to find the difference of two algebraic expressions.
What is the Difference of Algebraic Expressions?
The difference of two algebraic expressions is the result of subtracting one expression from another. It is denoted by the symbol - or −. For example, if we have two algebraic expressions 12a^2b and -5a^2b, we need to find their difference.
How to Find the Difference of Algebraic Expressions
To find the difference of two algebraic expressions, we need to follow a simple step-by-step process. Here are the steps:
- Identify the expressions: The first step is to identify the two algebraic expressions that we need to find the difference of.
- Subtract the expressions: Once we have identified the expressions, we need to subtract one expression from another. This is done by subtracting the coefficients of like terms.
- Simplify the expression: After subtracting the expressions, we need to simplify the resulting expression by combining like terms.
Applying the Concept to the Given Problem
Now that we have understood the concept of finding the difference of algebraic expressions, let's apply it to the given problem. We need to find the difference of 12a^2b and -5a^2b.
Option A: (12-5)a^2b
Option A is (12-5)a^2b. This option suggests that we need to subtract 5 from 12 and then multiply the result by a^2b. However, this is not the correct way to find the difference of algebraic expressions.
Option B: (12+5)a4b2
Option B is (12+5)a^4b^2. This option suggests that we need to add 5 to 12 and then multiply the result by a^4b^2. However, this is not the correct way to find the difference of algebraic expressions.
Option C: (12+5)a^2b
Option C is (12+5)a^2b. This option suggests that we need to add 5 to 12 and then multiply the result by a^2b. However, this is not the correct way to find the difference of algebraic expressions.
Option D: (12-5)a4b2
Option D is (12-5)a^4b^2. This option suggests that we need to subtract 5 from 12 and then multiply the result by a^4b^2. However, this is not the correct way to find the difference of algebraic expressions.
The Correct Answer
The correct answer is Option A: (12-5)a^2b. This option suggests that we need to subtract 5 from 12 and then multiply the result by a^2b. This is the correct way to find the difference of algebraic expressions.
Conclusion
In conclusion, finding the difference of algebraic expressions is a simple process that involves subtracting one expression from another. We need to identify the expressions, subtract the coefficients of like terms, and simplify the resulting expression by combining like terms. The correct answer to the given problem is Option A: (12-5)a^2b.
Final Answer
The final answer is Option A: (12-5)a^2b.
Introduction
Finding the difference of algebraic expressions is a fundamental concept in mathematics. In this article, we will answer some frequently asked questions (FAQs) on this topic.
Q: What is the difference of algebraic expressions?
A: The difference of two algebraic expressions is the result of subtracting one expression from another. It is denoted by the symbol - or −.
Q: How do I find the difference of two algebraic expressions?
A: To find the difference of two algebraic expressions, you need to follow these steps:
- Identify the expressions: Identify the two algebraic expressions that you need to find the difference of.
- Subtract the expressions: Subtract one expression from another by subtracting the coefficients of like terms.
- Simplify the expression: Simplify the resulting expression by combining like terms.
Q: What is the correct way to find the difference of algebraic expressions?
A: The correct way to find the difference of algebraic expressions is to subtract one expression from another by subtracting the coefficients of like terms. For example, if we have two algebraic expressions 12a^2b and -5a^2b, we need to subtract -5a^2b from 12a^2b to get the difference.
Q: Can I add the expressions instead of subtracting them?
A: No, you cannot add the expressions instead of subtracting them. Adding the expressions will give you the sum of the two expressions, not the difference.
Q: What is the difference between the sum and the difference of algebraic expressions?
A: The sum of two algebraic expressions is the result of adding one expression to another, while the difference of two algebraic expressions is the result of subtracting one expression from another.
Q: How do I simplify the resulting expression after finding the difference?
A: To simplify the resulting expression after finding the difference, you need to combine like terms. Like terms are terms that have the same variable and exponent.
Q: Can I use a calculator to find the difference of algebraic expressions?
A: Yes, you can use a calculator to find the difference of algebraic expressions. However, it is always a good idea to check your work by hand to ensure that you have the correct answer.
Q: What are some common mistakes to avoid when finding the difference of algebraic expressions?
A: Some common mistakes to avoid when finding the difference of algebraic expressions include:
- Adding the expressions instead of subtracting them
- Not combining like terms
- Not checking your work by hand
Conclusion
In conclusion, finding the difference of algebraic expressions is a simple process that involves subtracting one expression from another. By following the steps outlined in this article, you can find the difference of algebraic expressions with ease.
Final Tips
- Practice, practice, practice: The more you practice finding the difference of algebraic expressions, the more comfortable you will become with the process.
- Check your work: Always check your work by hand to ensure that you have the correct answer.
- Use a calculator: You can use a calculator to find the difference of algebraic expressions, but it is always a good idea to check your work by hand.