Algebaic term and Numeric term

We shall now put in a systematic form what we have learnt above about how expressions are formed. For this purpose, we need to understand what terms of an expression and their factors are.

Consider the expression (4x + 5) in forming this expression, we first formed 4x separately as a of 4 and x and then 5 to it.

Similarly consider the expression (3x2+7y)

Here we first formed 3x2 separately as a product of , x and x. We then formed 7y separately as a product of and y.

Having formed 3x2 and 7y separately, we added them to get the expression.

You will find that the expressions we deal with can always be seen this way.

They have parts which are formed separately and then added. Such parts of an expression which are formed separately first and then added are known as terms.

Look at the expression (4x2-3xy)

we say that it has two terms, 4x2 and –3xy. The term 4x2 is a product of , x and x, and the term −3xy is a product of , x and y.

Terms are added to form expressions: Just as the terms 4x and 5 are addedmultiply to form the expression (4x + 5), the terms (4x2) and -3xy are addedsubtract to give the expression (4x2-3xy)

This is because 4x2 + (–3xy) = 4x2 – 3xy.

Like and Unlike Terms

When terms have the same algebraic factors, they are likeunlike terms.

When terms have different algebraic factors, they are unlikelike terms.

For example:

In the expression 2xy – 3x + 5xy – 4, look at the terms 2xy and 5xy. The factors of 2xy are , x and y. The factors of 5xy are ,x and y. Thus their algebraic (i.e., those which contain variables) factors are the same and hence they are like terms.

On the other hand the terms 2xy and –3x, have different algebraic factors. They are unlikelike terms. Similarly, the terms 2xy and 4, are unlike terms. Also, the terms –3x and 4 are unlike terms.

Group the like terms together from the following: 12x, 12, – 25x, – 25, – 25y, 1, x, 12y, y

Instruction