## Algebraic Expressions

Consider the following algebraic expression:

\(2x^{3} + 3x^{2} + 4xy + 1\)

What are ‘x’ and ‘y’ over here? What are 1, 2, 3 and 4? They are letters and numbers but what do they represent? To understand what they represent, you should first understand what variables and constants are.

A **constant** is a value or number that never changes in an expression it’s constantly the same. For example, in the figure given above 36 and 82 are constant because its face value is 36 and 85 respectively. Its value never changes.

Then what are ‘x’ and ‘y’ here? They are varying quantities because you can substitute different values for these and therefore they are called variable. A **variable** is a letter representing some unknown; a variable always represents a number, but it carries varying values when written in an expression. By convention, mathematicians usually assign letters(not mandatory) at the end of the alphabet (such as x, y, and z) to be variables.

All algebraic expressions and terms consist of at least one variable. It is the variable which distinguishes an algebraic expression from an arithmetic one. The presence of a variable in a mathematical expression enables infinite possibilities to determine the value of the expression.

And what are algebraic expressions and terms? Is there a difference between the two? Let me give you an example. Let’s take an example of 2n and r².

Here 2n, r² and other examples like say 4xy, 2x² and such are different terms. A **term** is a grouping together of one or more factors. Here multiplication is the only thing connecting the number with the variables. And what do I mean by this?

Let’s take the number 4xy. Here 4, x and y are the factors of this number, where 4 is the coefficient or numerical factor. Don’t understand me? Okay let me assign values. Let x = 2 and y = 3. Now what is 4xy?

4 x 2 x 3 = ? Which is 24, In this case, 4xy is 24 and 4, 2 and 3 are its factors. 4 again can be written as 2 x 2.

4xy takes different values with different values of x and y. So, term is a combination of number and variable separated by multiplication or division. An **expression** is combination of such terms.

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