Like and Unlike Terms
How like and unlike terms are different from each other?
Like Terms:
When the terms have the same literal factors, they are called like terms.
For example: 4x, - 7x are like terms.
Definition of Like Terms:
The terms which have the same literal coefficients raised to the same powers but may only differ in numerical coefficient are called similar or like terms.
For Example:
(i) 3m and –7m are like terms.
(ii) z and \(\frac{3}{2}\)z are like terms.
Unlike Terms:
When the terms have the different literal factors, they are called unlike terms.
For example: xy, - 7xyz are unlike terms.
Definition of Unlike Terms:
The terms which do not have the same literal coefficients
raised to the same powers are called dissimilar
or unlike terms.
For Example:
(i) 9p and 9q are unlike terms
(ii) \(\frac{x}{3}\) and \(\frac{y}{3}\) are unlike terms
Solved examples on like and unlike terms:
Here, the like terms are 5x2y, – 9yx2 since each of them having the same literal coefficients x2y.
And the unlike terms are 4xy2, – xy since each of them having the different literal coefficients.
2. In algebraic expression 5x2 – 3y2 – 7x2 + 5xy + 4y2 + x2 – 2ab
Here, the like terms are 5x2, – 7x2, x2 and – 3y2, 4y2.
And the unlike terms are 5xy and – 2ab
3. Separate like & unlike terms from algebraic expression 5m2 – 3mn + 7m2n.
Here we see that all the terms of the given expression are unlike.
4. List out the like terms from each set:
(i) 7a, -5a, -8b, -a, a/3
7a, -5a, -a, a/3 are the set of like terms.
(ii) –xy, 3y, 5xy, -x, -xy/11
–xy, 5xy, -xy/11 are the set of like terms.
(iii) 2p3q2, -4p2q3, 7q2p3, -2p3q22p3q2, 7q2p3, -2p3q2 are the set of like terms.
(iv) 2x2y, 3x3y, 2xy2, 4yx2, -2x2y, -3yx2
2x2y, 4yx2, -2x2y, -3yx2 are the set of like terms.
(v) a2b3, -5a3b2, 7a3b2, 11a3b3, -3b2a3
-5a3b2, 7a3b2, -3b2a3 are the set of like terms.
5. Which of the following are like terms ?
(i) 3xy, -2y, 8x
(ii) 5mn, mn, -3mn
(iii) -7pq, 5pq, 6p
(iv) -4uv, v, 5uv
Solution:
Like terms have the same literal factors.
Thus, the option (ii) satisfies the condition.
Note: We can add or subtract like terms but in case of unlike terms we cannot add or subtract.
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