Addition And Subtraction Of Algebraic Expressions

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

2x + 5x

= (2 \times x) + (5 \times x)

= (2 + 5) \times x (using distributive law)

= 7 × x = 7x

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: 12p2 – 9p + 5p – 4p2 – 7p + 10

Solution

First we have to rearrange the terms.

12p2 – 4p2 + 5p – 9p – 7p + 10

= (12 – 4) p2 + (5 – 9 – 7) p + 10

= 8p2 + (– 4 – 7) p + 10

= 8p2 + (–11) p + 10

= 8p2 – 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– 5b2 – 3a2 from 5a2 + 3b2 – ab

Solution

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