How to Identify Like Terms and Unlike Terms with Rules and Solved Examples
The primary meaning of these two words is like and unlike. In other words, it means that they are both the same or they are different. For example, the letter “B” in the English language has a shape which is like “a” in the Arabic language. The same letter B has a form which is different from A or B on another hand. In mathematics, it also has a similar meaning as between two numbers but its meaning becomes stronger as it refers to objects which are not at all alike only difference consists of their numerical differences called arithmetic operations.
Like and Unlike Terms
Algebra is the study of mathematical concepts using a method of symbolic expression, wherein relations between quantities are expressed in terms of mathematical operations with symbols. Like and unlike terms can be found in various contexts, which forces students to consider their definitions and how they apply to the context or aim they are intended to serve.
What are Like Terms?
The like terms refer to terms in an algebraic expression with the same variable raised to the same power. Algebraic-like terms are terms that are similar to each other. These like terms in the algebraic expression can be combined to simplify the expression to derive the answer in a simple manner.
Like Terms Examples:
$14y-2y$: Here all the variables are $y$ to the power 1.
$14x^2+9x^2-x^2$: Here all the variables are $x$ to the power 2.
Rules of Addition of Like Terms
Consider another expression $5z + 12z + 32z$, here we see that the variables have the same exponent and the coefficients are also the same. We can further simplify this expression by adding the same variables from each other. This is possible since the variables and the exponents are the same. Hence, after simplifying the expression we get $(5 + 12 + 32)z = 49z$. The process of simplifying the expression is known as combining like terms.
Addition of Like Terms
What are Unlike Terms?
Unlike terms refers to terms in an algebraic expression that does not have the same literal coefficients and cannot be raised to the same power.
Examples of unlike terms:
$3x+9y$
$13x+2xy-4y$
For example, the algebraic expression $3x + 9y$ where $x$ and $y$ are two different variables and different coefficients are known as unlike algebraic terms.
Rules of Addition for Unlike Terms
The simplification of expressions or combining like terms cannot be done on unlike terms, as the variables and exponents are not similar. For example, $8xy + 6y - 9x - 10x^2$, as seen here, there are different variables, exponents, and coefficients. This expression cannot be simplified as all the terms are different from each other.
Hence, for unlike terms there are no rules as they can’t be added.
How Can Like Terms and Unlike Terms be Separated?
When you focus on the words' variables, it is simple to distinguish between similar terms and those that are not. The variable component of like phrases will be the same, while the variable part of unlike terms will be different.
Similarities and Differences between Like and Unlike Terms
Like terms and unlike terms are expressions that contain different variables, but whose coefficients are all either positive or negative multiples of the same number.
In the case of like terms, the coefficients must be multiplied by the same number while in unlike terms examples they must be multiplied by different numbers. An example of like terms is: -3x + (-2x)
The only difference between these two terms is that the first term has a negative coefficient and the second term has a positive coefficient. One of the unlike terms examples is -4x + (-12x) + 8y
Steps to Find Like Terms
Isolate the variable.
Collect all like terms on one side of the equation or workbook page.
Connect like terms using any Maths operation (addition, subtraction, multiplication, or division) after the variable has been isolated.
Simplify and solve for x in terms of y.
Steps to Find Unlike Terms
Isolate the variable.
Collect all unlike terms on one side of the equation.
Find the coefficient of largest/smallest coefficient in each term found.
Simplify and solve for x in terms of y.
Some Examples of like Terms and Unlike Terms
These strategies are used to find these types of expressions and relate them to their intended context or target area: all problems can be done while solving a like and unlike terms worksheet.
Solved Examples
Q 1. What are the like and unlike terms in the given algebraic expression 5x2y + 4xy2 – xy – 9yx2 ?
Ans: Here, the terms are 5x2y, – 9yx2 since each of them has the same literal coefficient x2y.
And the unlike terms are 4xy2, – xy since each of them has different literal coefficients.
Q 2. Find out the like and unlike terms in the given algebraic expression 5x2 – 3y2 – 7x2 + 5xy + 4y2 + x2 – 2ab?
Ans: Here, the like terms are 5x2, – 7x2, x2 and – 3y2, 4y2.
And the unlike terms are 5xy and – 2ab
Q 3. In the algebraic expression, identify the like terms - 10xy + 3x3 + 21xy + 2x - xy - 6
Ans: Like terms: 10xy + 21xy - xy = 30xy
unlike terms: 7y - 5xy - 12x
Practice Questions:
Q 1. Group the like terms together:
(A)5x, -7y, -x, y/2, 5x/7, x and y
(B)2/3ab, -3ab, 5bc, -2/5bc, bc/4 and ab
(C)2/6ab
Ans: 5x, -x, 5x/7, x and -7y, y/2, y ( Option A )
Q 2. List out the like terms from each set:
(A)2m2n3, -3m2n3, 4mn2, 7m2n3
(B)12a2b, 3ab2, 4ba2, 2a2b
Ans: Like terms- 2m2n3, -3m2n3, 7m2n3
Unlike terms- 12a2b, 4ba2, 2a2b
Q 3. State whether the following statements are true or false:
(A) 8z has two terms 8 and z.
(B) Expression 10 + k has two terms 10 and k.
(C) xy and –yx are like terms.
Ans: False, True, True
Summary
A term in an algebraic expression may contain only a constant, just one variable, the product of two or more variables, or the product of the variable and the constant part. A single term can be created by combining one or more similar terms, but two dissimilar terms cannot be combined to create a single term. Like and unlike terms are discussed in brief with their examples. This article also contains some solved examples of the addition of like terms.
FAQs on Like Terms and Unlike Terms in Algebra
1. What are like terms in algebra?
Like terms are algebraic terms that have exactly the same variables raised to the same powers. Only the numerical coefficients can be different.
For example:
- 3x and 7x are like terms (same variable x).
- 5a² and −2a² are like terms (same variable and exponent).
- 4xy and 9xy are like terms (same variables and powers).
2. What are unlike terms?
Unlike terms are algebraic terms that have different variables or different powers of the same variable. These terms cannot be combined by addition or subtraction.
For example:
- 3x and 3y are unlike terms (different variables).
- 4a and 4a² are unlike terms (different exponents).
- 2xy and 2x are unlike terms (different variable combinations).
3. How do you identify like and unlike terms?
To identify like and unlike terms, compare the variables and their exponents in each term.
Follow these steps:
- Ignore the numerical coefficients.
- Check if the variables are exactly the same.
- Check if the exponents of the variables are the same.
4. How do you combine like terms?
You combine like terms by adding or subtracting their coefficients while keeping the variable part unchanged.
Example:
Combine 4x + 7x:
- Add coefficients: 4 + 7 = 11
- Keep the variable x
Another example:
5a² − 2a² = (5 − 2)a² = 3a².
5. Why can only like terms be added or subtracted?
Only like terms can be added or subtracted because they represent the same algebraic quantity.
For example:
- 3 apples + 5 apples = 8 apples (same item).
- 3x + 5y cannot be simplified because x and y represent different variables.
6. Can constants be like terms?
Yes, all constant numbers are like terms because they have no variables.
For example:
- 7 and −3 are like terms.
- 10 + 5 − 2 = 13
7. Are 2xy and 2yx like terms?
Yes, 2xy and 2yx are like terms because multiplication of variables is commutative.
Since xy = yx, both terms have the same variables raised to the same powers:
- 2xy
- 2yx
2xy + 2yx = 4xy.
8. What is the difference between like terms and unlike terms?
The difference between like and unlike terms is that like terms have identical variables and exponents, while unlike terms do not.
Comparison:
- Like terms: 6x and −2x (same variable x).
- Unlike terms: 6x and 6x² (different powers of x).
9. Can you give an example of simplifying an expression using like terms?
Simplifying an expression using like terms means combining terms with the same variables and exponents.
Example:
Simplify 3x + 5y + 2x − y:
- Combine x terms: 3x + 2x = 5x
- Combine y terms: 5y − y = 4y
10. What are common mistakes when combining like terms?
A common mistake when combining like terms is adding variables instead of only adding coefficients.
Common errors include:
- Thinking 3x + 2x = 5x² (incorrect).
- Combining unlike terms like 4a + 4b = 8ab (incorrect).
- Ignoring exponents, such as treating a and a² as like terms.
