Subtract.$ (5n + 5) - (5n + 5) $
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Introduction
In algebra, simplifying expressions is a crucial step in solving equations and inequalities. One of the fundamental concepts in simplifying expressions is subtracting like terms. In this article, we will delve into the world of subtracting like terms, focusing on the expression Subtract.$ (5n + 5) - (5n + 5) $. We will explore the concept of like terms, the rules for subtracting them, and provide step-by-step examples to illustrate the process.
What are Like Terms?
Like terms are algebraic expressions that have the same variable(s) raised to the same power. In other words, they are terms that have the same combination of variables and coefficients. For example, 2x and 5x are like terms because they both have the variable x raised to the power of 1. Similarly, 3y^2 and 4y^2 are like terms because they both have the variable y raised to the power of 2.
Subtracting Like Terms: The Rules
When subtracting like terms, we follow a simple rule: we subtract the coefficients of the like terms. The variable(s) and the exponent(s) remain the same. For example, if we have the expression 2x - 5x, we can subtract the coefficients (2 and 5) to get -3x. The variable x remains the same.
Subtracting the Expression (5n + 5) - (5n + 5)
Now, let's apply the rules of subtracting like terms to the expression Subtract.$ (5n + 5) - (5n + 5) $. We can start by identifying the like terms in the expression. In this case, the like terms are 5n and -5n, and the constants are 5 and -5.
Step 1: Distribute the Negative Sign
When subtracting a term, we can distribute the negative sign to the terms inside the parentheses. This gives us:
- (5n + 5) = -5n - 5
Step 2: Subtract the Like Terms
Now that we have distributed the negative sign, we can subtract the like terms. In this case, we have 5n and -5n, which are like terms. We can subtract the coefficients (5 and -5) to get 0n or simply 0. The variable n remains the same.
5n - (-5n) = 5n + 5n = 10n
Step 3: Subtract the Constants
Next, we can subtract the constants. In this case, we have 5 and -5, which are like terms. We can subtract the coefficients (5 and -5) to get 0. The constant term disappears.
5 - (-5) = 5 + 5 = 10
Step 4: Combine the Results
Finally, we can combine the results of the previous steps. We have 10n and 10, which are like terms. We can combine them to get 10n + 10.
10n + 10
Conclusion
In conclusion, subtracting like terms is a fundamental concept in algebra that allows us to simplify expressions. By following the rules of subtracting like terms, we can simplify complex expressions and solve equations and inequalities. In this article, we applied the rules of subtracting like terms to the expression Subtract.$ (5n + 5) - (5n + 5) $ and arrived at the simplified expression 10n + 10. We hope that this article has provided a comprehensive guide to simplifying algebraic expressions using the concept of like terms.
Frequently Asked Questions
Q: What are like terms?
A: Like terms are algebraic expressions that have the same variable(s) raised to the same power.
Q: How do I subtract like terms?
A: To subtract like terms, we follow a simple rule: we subtract the coefficients of the like terms. The variable(s) and the exponent(s) remain the same.
Q: What is the result of subtracting (5n + 5) - (5n + 5)?
A: The result of subtracting (5n + 5) - (5n + 5) is 10n + 10.
Additional Resources
For more information on subtracting like terms, we recommend the following resources:
- Khan Academy: Subtracting Like Terms
- Mathway: Subtracting Like Terms
- Algebra.com: Subtracting Like Terms
Final Thoughts
In conclusion, subtracting like terms is a fundamental concept in algebra that allows us to simplify expressions. By following the rules of subtracting like terms, we can simplify complex expressions and solve equations and inequalities. We hope that this article has provided a comprehensive guide to simplifying algebraic expressions using the concept of like terms.
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Q: What are like terms?
A: Like terms are algebraic expressions that have the same variable(s) raised to the same power. For example, 2x and 5x are like terms because they both have the variable x raised to the power of 1.
Q: How do I identify like terms in an expression?
A: To identify like terms in an expression, look for terms that have the same variable(s) raised to the same power. For example, in the expression 3x + 2x + 4y, the like terms are 3x and 2x because they both have the variable x raised to the power of 1.
Q: How do I subtract like terms?
A: To subtract like terms, follow these steps:
- Identify the like terms in the expression.
- Subtract the coefficients of the like terms.
- The variable(s) and the exponent(s) remain the same.
For example, if we have the expression 2x - 5x, we can subtract the coefficients (2 and 5) to get -3x.
Q: What is the result of subtracting (5n + 5) - (5n + 5)?
A: The result of subtracting (5n + 5) - (5n + 5) is 10n + 10. This is because we can distribute the negative sign to the terms inside the parentheses, and then subtract the like terms.
Q: Can I subtract like terms with different coefficients?
A: Yes, you can subtract like terms with different coefficients. For example, if we have the expression 3x - 2x, we can subtract the coefficients (3 and 2) to get x.
Q: Can I subtract like terms with different variables?
A: No, you cannot subtract like terms with different variables. For example, 2x and 3y are not like terms because they have different variables.
Q: What is the difference between subtracting like terms and combining like terms?
A: Subtracting like terms involves subtracting the coefficients of the like terms, while combining like terms involves adding the coefficients of the like terms. For example, if we have the expression 2x + 3x, we can combine the like terms to get 5x.
Q: Can I use the distributive property to subtract like terms?
A: Yes, you can use the distributive property to subtract like terms. For example, if we have the expression 2x - 3x, we can use the distributive property to get 2x - 3x = (2 - 3)x = -x.
Q: What is the importance of subtracting like terms in algebra?
A: Subtracting like terms is an essential concept in algebra because it allows us to simplify expressions and solve equations and inequalities. By subtracting like terms, we can eliminate variables and constants, making it easier to solve problems.
Q: Can I use a calculator to subtract like terms?
A: Yes, you can use a calculator to subtract like terms. However, it's 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 subtracting like terms?
A: Some common mistakes to avoid when subtracting like terms include:
- Not identifying like terms correctly
- Subtracting coefficients incorrectly
- Not distributing the negative sign correctly
- Not combining like terms correctly
By avoiding these mistakes, you can ensure that you get the correct answer when subtracting like terms.
Conclusion
In conclusion, subtracting like terms is a fundamental concept in algebra that allows us to simplify expressions and solve equations and inequalities. By following the rules of subtracting like terms, we can eliminate variables and constants, making it easier to solve problems. We hope that this article has provided a comprehensive guide to subtracting like terms and has helped you to understand this important concept in algebra.