Operations in algebra (Addition and Subtraction)

There are four operations which can be performed on variables. These are addition, subtraction, multiplication and division. Repeated multiplication and division are parts of exponents.

Let us consider three arithmetic expressions.
1×3+2×3+3×3+4×3 = 3 + 6 + 9 + 12 = 30
1×5+2×5+3×5+4×5 = 5 + 10 + 15 + 20 = 50
1×8+2×8+3×8+4×8 = 8 + 16 + 24 + 32 = 80
When we look at the above expressions we find that 3 changes to 5 and 5 changes to 8.

As the value changes we can put a symbolic constant in place of it. Let it be a. Then the expression turns to
1×a+2×a+3×a+4×a
We can write
1a+2a+3a+4a
as the symbol of product in algebra can be replaced by nothing.

The numbers occurring in front of the symbolic constants are called the coefficients. They are also called coefficients if the symbolic constants are replaced by variables.

To perform the operation of addition simply add the coefficients of the symbolic constants.

Here we get (1+2+3+4)a = 10a

When we put different values of a, we get
a=3, 10a = 30
a=5, 10a = 50
a=8, 10a = 80.
Hence we have verified the operation.

Subtraction
To perform subtraction simply do subtraction for the coefficients.
23a − 7a = (23 − 7)a = 16a

Like and unlike terms

When the symbol for the symbolic constant or the variables are same for all the terms then the terms are called the like terms. Else they are unlike terms.

3a and 6a are like terms. Some examples of like terms are
3d and 7d, 23ad and 67ad, 3x and 7x, 4xy and 5xy, etc.
When the variables or symbolic constants are different for the considering terms then the terms are called unlike terms.Some examples of unlike terms are
3x and 6y, 56df and 78hu, etc.

Rules for addition and subtraction

1. Group the like terms.
2. Add or subtract the coefficients.
3. Only like terms can be added to or subtracted from each other.

Example 1:
Add 2x + 3y + 4z and 3x + 7x + 7y + 6z
2x + 3y + 4z + 3x + 7x + 7y + 6z
= 2x + 3x + 7x + 3y + 7y + 4z + 6z
= (2+3+7)x + (3+7)y + (4+6)z
= 12x + 10y + 10z