Like and Unlike Terms

How like and unlike terms are different from each other?

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  3/2 z are like 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) x/3 and y/3 are unlike terms

Solved examples on like and unlike terms:

1. In algebraic expression 5x²y + 4xy² – xy – 9yx²

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, -2p³q²

2p³q², 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.

Note: We can add or subtract like terms but in case of unlike terms we cannot add or subtract.

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● Terms

Like and Unlike Terms

Like Terms

Addition of Like Terms

Subtraction of Like Terms

Adding and Subtracting Like Terms

Unlike Terms

Addition of Unlike Terms

Subtraction of Unlike Terms

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