# 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.

Like Terms

Subtraction of Like Terms

Unlike Terms

Subtraction of Unlike Terms

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