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Like and Unlike algebraic terms are the essential part of algebra. Algebraic expressions are a set of terms that have been combined using multiple operations like addition, subtraction, multiplication, and division. As defined by Algebra, like terms are terms containing the same variable which has been raised to the same power. On the other hand, unlike terms are those terms whose literal coefficients are different and which cannot be raised to the same power.
Read Also: Pair of Linear Equations in Two Variables Important Question
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Key Terms: Like Terms, Unlike Terms, Addition, Algebraic Expression, Literal Coefficient, Variable, Constant
Like Terms in Algebra
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In Algebra, like terms can be defined as those terms that contain the same variable raised to the same power. The only thing that alters in algebraic expression is the numerical coefficients. Like terms can be used to simplify algebraic equations which in terms makes it easier to solve the equation.
For example, 4x + 10x is an algebraic expression with like terms. Similar terms can be used to simplify the given algebraic expression. Which in terms gives the result as 14x. Similarly, we can execute all arithmetic operations
From the above explanation, it can be concluded that algebraic terms with the same variables can be added to one another. The reason why they were being added is due to the similarity in their coefficients. Like terms are those that have the same variables.
For Example
- 7xy, 2xy, -6xy are like terms
Each has the same literal coefficient that is xy
- 0.6a, 9a, -18a, a are like terms
Each has the same literal coefficient that is a
- 18x, 5x, 6.5x, 0.85x are like terms
Each has the same literal coefficient that is x
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Unlike Terms in Algebra
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Unlike terms are those algebraic terms that do not have the same literal coefficients and they cannot be raised to the same power. 14x + 19y is an algebraic expression but they are unlike terms because of the different variables x and y.
For Example
- 9p and 56q are unlike terms
- p/3 and q/3 are unlike terms
- 61ab, 16a, 9ac are unlike terms
- 2z, 52x, 12y are unlike terms.
Addition of Like Terms and Unlike Terms in Algebra
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While adding algebraic expressions, a certain set of rules jump in. We first need to simplify the equation by adding all the like terms and then continue the equation. An algebraic expression can be added just by combining all the like terms first.
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Addition of Algebraic Expressions
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The addition of algebraic expressions is similar to adding numbers.
While adding algebraic expressions an additional step needs to be done which is to categorize the like and unlike terms. After that, we need to add the terms that are similar. Like terms are those terms that have the same power for the same variables. In terms that are similar to each other in them, only the numerical coefficient can be changed.
The Following are the Steps to Use While Adding Algebraic Expressions Using the Horizontal Method:
- Step 1: Arrange all of the expressions in a horizontal line by bracketing them and adding an extra sign in between.
- Step 2: From all of the expressions, group all of the like terms together and rewrite the expression.
- Step 3: After the common variable, add the numerical coefficients of all the like terms.
- Step 4: Rewrite the simplified expression and double-check that all of the terms in the final solution are unlike terms.
Read More: Addition of Two Real Numbers
Addition of Two Unlike Terms in Algebra
Below are a few examples of adding like and unlike terms:
Example 1: Add terms x and y.
Sol: To determine the sum of the given unlike terms x and y, we need to interlink both terms with an additional sign to get the result as x + y.
Hence, the sum of these unlike terms x and y = x + y.
Example 2: Subtract 24xy from 28xy
Sol: To find the difference we need to subtract the coefficient (28 – 24) = 4
Therefore, 28xy – 24xy = 4xy
Example 3: Difference of 15ab from 45ab
Sol: To find the difference we need to subtract the coefficient 45 – 15 = 30
Therefore, 45ab – 15ab = 30ab
Example 4: Add the like terms & then simplify 7a – 3b + 4ab + 9b – 6ab – 3a
Sol:
= 7a – 3a – 3b + 9b + 4ab – 6ab → we can arrange like terms in this way
= (7 - 3)a + (-3 + 9)b + (4 - 6)ab → we can combine like terms like this
= (4)a + (6)b + (-2)ab → simplify
= 4a + 6b - 2ab → Answer
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Things to Remember
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- Algebraic expressions in mathematics can be added in the same manner, as any numbers and the sum can be determined.
- While adding algebraic expressions we combine all the like terms first and then add them.
- Like terms are ones that have the same variables and exponent power. These variables' coefficients can be different.
- Unlike terms are those in which the variables and exponents are different from one another.
- In a given condition when the coefficient is different, the variables are distinct (two variables), and the exponent powers are different in an expression.
Sample Questions
Ques. In algebraic expressions 5x2y + 4xy2 – xy – 9yx2 list out the like and unlike terms. [2 Marks]
Ans: Here, the like terms are 5x2y, – 9yx2 since each of them has the same literal coefficients x2y.
And the unlike terms are 4xy2, – xy since each of them has different literal coefficients.
Ques. In algebraic expressions 5x2 – 3y2 – 7x2 + 5xy + 4y2 + x2 – 2ab list out the like and unlike terms. [1 Mark]
Ans:
Here, the like terms are 5x2, – 7x2, x2 and – 3y2, 4y2.
And the unlike terms are 5xy and – 2ab
Ques. List out the like terms from each set: [3 Marks}
(i) 7a, -5a, -8b, -a, a/3
(ii) –xy, 3y, 5xy, -x, -xy/11
(iii) 2p3q2, -4p2q3, 7q2p3, -2p3q2
(iv) 2x2y, 3x3y, 2xy2, 4yx2, -2x2y, -3yx2
(v) a2b3, -5a3b2, 7a3b2, 11a3b3, -3b2a3
Ans:
- 7a, -5a, -a, a/3 are the set of like terms.
- –xy, 5xy, -xy/11 are the set of like terms.
- 2p3q2, 7q2p3, -2p3q2 are the set of like terms.
- 2x2y, 4yx2, -2x2y, -3yx2 are the set of like terms.
- -5a3b2, 7a3b2, -3b2a3 are the set of like terms.
Ques. Classify into monomials, binomials and trinomials. [3 Marks]
(i) 4y − 7z
(ii) y2
(iii) x + y − xy
(iv) 100
(v)ab − a − b
(vi) 5 − 3t
(vii) 4p2q − 4pq2
(viii) 7mn
(ix) z2 − 3z + 8
(x) a2 + b2
(xi) z2 + z
(xii) 1 + x + x2
Ans:
The monomials, binomials, and trinomials have 1, 2, and 3 unlike terms in it respectively.
(i) 4y − 7z
Binomial
(ii) y2
Monomial
(iii) x + y − xy
Trinomial
(iv) 100
Monomial
(v) ab − a − b
Trinomial
(vi) 5 − 3t
Binomial
(vii) 4p2q − 4pq2
Binomial
(viii) 7mn
Monomial
(ix) z2 − 3z + 8
Trinomial
(x) a2 + b2
Binomial
(xi) z2 + z
Binomial
(xii) 1 + x + x2
Trinomial
Ques. Add: [3 Marks]
(i) 3mn, − 5mn, 8mn, −4mn
(ii) t − 8tz, 3tz − z, z − t
(iii) − 7mn + 5, 12mn + 2, 9mn − 8, − 2mn − 3
Ans:
(i) 3mn + (−5mn) + 8mn + (−4mn) = mn (3 − 5 + 8 − 4)
= 2mn
(ii) (t − 8tz) + (3tz − z) + (z − t) = t − 8tz + 3tz − z + z − t
= t − t − 8tz + 3tz − z + z
= t (1 − 1) + tz (− 8 + 3) + z (− 1 + 1)
= −5tz
(iii) (− 7mn + 5) + (12mn + 2) + (9mn − 8) + (− 2mn − 3)
= − 7mn + 5 + 12mn + 2 + 9mn − 8 − 2mn − 3
= − 7mn + 12mn + 9mn − 2mn + 5 + 2 − 8 − 3
= mn (− 7 + 12 + 9 − 2) + (5 + 2 − 8 − 3)
= 12mn − 4
Ques. Subtract: [4 Marks]
(i) 5a2 − 7ab + 5b2 from 3ab − 2a2 −2b2
(ii) 4pq − 5q2 − 3p2 from 5p2 + 3q2 − pq
Ans:
(i) (3ab − 2a2 − 2b2) − (5a2− 7ab + 5b2)
= 3ab − 2a2 − 2b2 − 5a2 + 7ab − 5 b2
= 3ab + 7ab − 2a2 − 5a2 − 2b2 − 5 b2
= 10ab − 7a2 − 7b2
(ii) 4pq − 5q2 − 3p2 from 5p2 + 3q2 − pq
(5p2 + 3q2 − pq) − (4pq − 5q2− 3p2)
= 5p2 + 3q2 − pq − 4pq + 5q2 + 3p2
= 5p2 + 3p2 + 3q2 + 5q2 − pq − 4pq
= 8p2 + 8q2 − 5pq
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