Identify The Like And Unlike Terms And Write Them In The Tabular Form. (a) 17, Yx, Y, Zx, Z, 7xy, 78yx (b) 9y, -y, -3, -3x, Z, -2017 (c) A, -50, -55, -25a, -b, -12ab (d) 2xy, 15yz, -5x, -15y
5. Identify the Like and Unlike Terms and Write Them in Tabular Form
Understanding Like and Unlike Terms
In algebra, like terms are expressions that have the same variable(s) raised to the same power. Unlike terms, on the other hand, are expressions that have different variables or variables raised to different powers. Identifying like and unlike terms is an essential step in simplifying algebraic expressions and solving equations.
Example (a) - 17, yx, y, zx, z, 7xy, 78yx
To identify like and unlike terms in the given expression, we need to look for common variables and their powers.
- Like Terms: yx, 7xy, 78yx (all have the variable x and y)
- Unlike Terms: 17, y, zx, z (no common variables)
| Like Terms | Unlike Terms |
|---|---|
| yx, 7xy, 78yx | 17, y, zx, z |
Example (b) - 9y, -y, -3, -3x, z, -2017
Now, let's identify like and unlike terms in the given expression.
- Like Terms: 9y, -y (both have the variable y)
- Unlike Terms: -3, -3x, z, -2017 (no common variables)
| Like Terms | Unlike Terms |
|---|---|
| 9y, -y | -3, -3x, z, -2017 |
Example (c) - a, -50, -55, -25a, -b, -12ab
To identify like and unlike terms in the given expression, we need to look for common variables and their powers.
- Like Terms: -25a, -12ab (both have the variable a)
- Unlike Terms: a, -50, -55, -b (no common variables)
| Like Terms | Unlike Terms |
|---|---|
| -25a, -12ab | a, -50, -55, -b |
Example (d) - 2xy, 15yz, -5x, -15y
Now, let's identify like and unlike terms in the given expression.
- Like Terms: -5x (no common variables with other terms)
- Unlike Terms: 2xy, 15yz, -15y (no common variables)
| Like Terms | Unlike Terms |
|---|---|
| -5x | 2xy, 15yz, -15y |
Conclusion
In conclusion, identifying like and unlike terms is an essential step in simplifying algebraic expressions and solving equations. By recognizing common variables and their powers, we can group like terms together and simplify the expression. In this article, we have identified like and unlike terms in four different expressions and written them in tabular form.
5. Identify the Like and Unlike Terms and Write Them in Tabular Form: Q&A
Frequently Asked Questions
In this section, we will address some of the most common questions related to identifying like and unlike terms.
Q1: What are like terms in algebra?
A1: Like terms in algebra are expressions that have the same variable(s) raised to the same power. For example, 2x and 4x are like terms because they both have the variable x.
Q2: What are unlike terms in algebra?
A2: Unlike terms in algebra are expressions that have different variables or variables raised to different powers. For example, 2x and 3y are unlike terms because they have different variables.
Q3: How do I identify like and unlike terms in an algebraic expression?
A3: To identify like and unlike terms in an algebraic expression, you need to look for common variables and their powers. Group the terms that have the same variable(s) raised to the same power together, and those that do not have common variables are unlike terms.
Q4: Can a term be both like and unlike at the same time?
A4: No, a term cannot be both like and unlike at the same time. If a term has a common variable with another term, it is a like term. If it does not have a common variable with any other term, it is an unlike term.
Q5: Why is it important to identify like and unlike terms?
A5: Identifying like and unlike terms is essential in simplifying algebraic expressions and solving equations. By grouping like terms together, you can combine their coefficients and simplify the expression.
Q6: Can I have multiple like terms in an algebraic expression?
A6: Yes, you can have multiple like terms in an algebraic expression. For example, 2x, 4x, and 6x are all like terms because they have the same variable x.
Q7: How do I write like and unlike terms in a tabular form?
A7: To write like and unlike terms in a tabular form, create two columns: one for like terms and one for unlike terms. List the like terms in the first column and the unlike terms in the second column.
Q8: Can I have zero as a coefficient in a like term?
A8: Yes, you can have zero as a coefficient in a like term. For example, 0x and 4x are like terms because they have the same variable x.
Q9: Can I have a negative coefficient in a like term?
A9: Yes, you can have a negative coefficient in a like term. For example, -3x and 2x are like terms because they have the same variable x.
Q10: Why is it important to simplify algebraic expressions?
A10: Simplifying algebraic expressions is essential in solving equations and solving problems in mathematics. By simplifying expressions, you can make it easier to solve for the unknown variable.
Conclusion
In conclusion, identifying like and unlike terms is an essential step in simplifying algebraic expressions and solving equations. By recognizing common variables and their powers, we can group like terms together and simplify the expression. In this article, we have addressed some of the most common questions related to identifying like and unlike terms.