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:

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.

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.

● Terms

Like and Unlike Terms

Like Terms

Addition of Like Terms

Subtraction of Like Terms

Adding and Subtracting Like Terms

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Addition of Unlike Terms

Subtraction of Unlike Terms

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Worksheet on Like and Unlike Terms

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Worksheet on Adding and Subtracting Like Terms

Worksheet on Combining Like Terms

Worksheet on Addition of Unlike Terms

Worksheet on Subtraction of Unlike Terms