**1. Addition of Like Terms**

If we have to add like terms then we can simply add their numerical coefficients and the result will also be a like term.

**Example**

Add 2x and 5x.

**Solution**

=

= (using distributive law)

=

**2. Subtraction of Like Terms**

If we have to subtract like terms then we can simply subtract their numerical coefficients and the result will also be a like term.

**Example**

Subtract 3p from 11p.

**Solution**

11p – 3p

= (11 – 3) p

= 8p

**3. Addition of unlike terms**

If we have to add the unlike terms then we just have to put an addition sign between the terms.

**Example**

Add 9y, 2x and 3

**Solution**

We will simply write it like this-

9y + 2x + 3

**4. Subtraction of Unlike Terms**

If we have to subtract the unlike terms then we just have to put minus sign between the terms.

**Example**

Subtract 9y from 21.

**Solution**

We will simply write it like this-

21 – 9y

**5. Addition of General Algebraic Expression**

To add the general algebraic expressions, we have to arrange them so that the like terms come together, then simplify the terms and the unlike terms will remain the same in the resultant expression.

**Example**

Simplify the expression: 12p^{2} – 9p + 5p – 4p^{2} – 7p + 10

**Solution**

First we have to rearrange the terms.

12p^{2} – 4p^{2} + 5p – 9p – 7p + 10

= (12 – 4) p^{2} + (5 – 9 – 7) p + 10

= 8p^{2} + (– 4 – 7) p + 10

= 8p^{2} + (–11) p + 10

= 8p^{2} – 11p + 10

**6. Subtraction of General Algebraic Expression**

While subtracting the algebraic expression from another algebraic expression, we have to arrange them according to the like terms then subtract them.

Subtraction is same as adding the inverse of the term.

**Example**

Subtract 4ab– 5b^{2} – 3a^{2} from 5a^{2} + 3b^{2} – ab

**Solution**

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