Combining Like Terms (Simplify)13. 5 X + 7 − 3 X + 2 = 5x + 7 - 3x + 2 = 5 X + 7 − 3 X + 2 = 14. 10 − A + 12 + 3 A = 10 - A + 12 + 3a = 10 − A + 12 + 3 A = 15. Y + 2 X + 3 Y − 10 = Y + 2x + 3y - 10 = Y + 2 X + 3 Y − 10 = 16. − 7 X + 2 − 3 X − 2 = -7x + 2 - 3x - 2 = − 7 X + 2 − 3 X − 2 =
What are Like Terms?
In algebra, like terms are terms that have the same variable 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. Similarly, 3y and 4y are like terms because they both have the variable y raised to the power of 1.
Why Combine Like Terms?
Combining like terms is an essential skill in algebra that helps simplify complex expressions. By combining like terms, we can rewrite an expression in a more concise and manageable form. This can make it easier to solve equations and inequalities, and can also help us to identify patterns and relationships between variables.
How to Combine Like Terms
To combine like terms, we need to follow a few simple steps:
- Identify the like terms: Look for terms that have the same variable raised to the same power.
- Add or subtract the coefficients: Add or subtract the coefficients of the like terms. For example, if we have 2x and 5x, we can add their coefficients to get 7x.
- Keep the variable the same: The variable remains the same, even if we add or subtract the coefficients.
Examples of Combining Like Terms
Let's work through some examples to see how to combine like terms.
Example 1: Combining Like Terms with Variables
Problem: $5x + 7 - 3x + 2 = $
Solution: To combine like terms, we need to identify the like terms, which are 5x and -3x. We can add their coefficients to get 2x. The other terms, 7 and 2, are not like terms, so we leave them as is.
Example 2: Combining Like Terms with Variables and Constants
Problem: $10 - a + 12 + 3a = $
Solution: To combine like terms, we need to identify the like terms, which are -a and 3a. We can add their coefficients to get 2a. The other terms, 10 and 12, are not like terms, so we leave them as is.
Example 3: Combining Like Terms with Variables and Constants
Problem: $y + 2x + 3y - 10 = $
Solution: To combine like terms, we need to identify the like terms, which are y and 3y. We can add their coefficients to get 4y. The other terms, 2x and -10, are not like terms, so we leave them as is.
Example 4: Combining Like Terms with Variables and Constants
Problem: $-7x + 2 - 3x - 2 = $
Solution: To combine like terms, we need to identify the like terms, which are -7x and -3x. We can add their coefficients to get -10x. The other terms, 2 and -2, are not like terms, so we leave them as is.
Tips and Tricks
- Make sure to identify all the like terms in an expression before combining them.
- Use the distributive property to simplify expressions before combining like terms.
- Combine like terms in the order of their coefficients, from smallest to largest.
Conclusion
Combining like terms is an essential skill in algebra that helps simplify complex expressions. By following the steps outlined in this article, you can combine like terms and rewrite expressions in a more concise and manageable form. Remember to identify all the like terms in an expression, add or subtract their coefficients, and keep the variable the same. With practice, you'll become proficient in combining like terms and solving equations and inequalities with ease.
Practice Problems
Try combining like terms in the following problems:
- $4x + 2 - 3x + 5 = $
- $-2y + 3 + 4y - 1 = $
- $x + 2y - 3x + 4y = $
- $-5x + 2 - 2x - 3 = $
Answer Key
Combining Like Terms: Q&A ==========================
Frequently Asked Questions
Q: What are like terms in algebra?
A: Like terms are terms that have the same variable 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: Why do we need to combine like terms?
A: Combining like terms helps simplify complex expressions and makes it easier to solve equations and inequalities. It also helps us to identify patterns and relationships between variables.
Q: How do I identify like terms in an expression?
A: To identify like terms, look for terms that have the same variable raised to the same power. For example, in the expression 2x + 3y - 4x + 2y, the like terms are 2x and -4x, and 3y and 2y.
Q: How do I combine like terms?
A: To combine like terms, add or subtract the coefficients of the like terms. For example, if we have 2x and -4x, we can add their coefficients to get -2x.
Q: What if I have a term with a variable raised to a power and another term with the same variable raised to a different power?
A: If you have a term with a variable raised to a power and another term with the same variable raised to a different power, they are not like terms. For example, 2x^2 and 3x are not like terms because they have the same variable raised to different powers.
Q: Can I combine like terms with variables and constants?
A: Yes, you can combine like terms with variables and constants. For example, in the expression 2x + 3y - 4x + 2y, you can combine the like terms 2x and -4x to get -2x, and the like terms 3y and 2y to get 5y.
Q: What if I have a negative sign in front of a term?
A: If you have a negative sign in front of a term, it becomes a positive sign when you combine like terms. For example, in the expression -2x + 3x, the negative sign in front of -2x becomes a positive sign when you combine the like terms to get x.
Q: Can I combine like terms with fractions?
A: Yes, you can combine like terms with fractions. For example, in the expression 1/2x + 1/3x, you can combine the like terms to get 5/6x.
Q: What if I have a term with a variable raised to a power and another term with the same variable raised to a power and a coefficient?
A: If you have a term with a variable raised to a power and another term with the same variable raised to a power and a coefficient, they are not like terms. For example, 2x^2 and 3x^2 are not like terms because they have the same variable raised to the same power, but the coefficient is different.
Q: Can I combine like terms with decimals?
A: Yes, you can combine like terms with decimals. For example, in the expression 2.5x + 3.2x, you can combine the like terms to get 5.7x.
Common Mistakes to Avoid
- Not identifying all the like terms in an expression
- Not adding or subtracting the coefficients of like terms correctly
- Not keeping the variable the same when combining like terms
- Combining like terms with variables and constants incorrectly
- Not considering negative signs when combining like terms
Conclusion
Combining like terms is an essential skill in algebra that helps simplify complex expressions. By following the steps outlined in this article, you can combine like terms and rewrite expressions in a more concise and manageable form. Remember to identify all the like terms in an expression, add or subtract their coefficients, and keep the variable the same. With practice, you'll become proficient in combining like terms and solving equations and inequalities with ease.
Practice Problems
Try combining like terms in the following problems:
- $4x + 2 - 3x + 5 = $
- $-2y + 3 + 4y - 1 = $
- $x + 2y - 3x + 4y = $
- $-5x + 2 - 2x - 3 = $