Properties of variables

Properties of variables with examples

Let’s review the properties using variables instead of numbers:

The properties above do NOT work with subtraction and division.

Distributive Property

This one is very important when working with algebraic expressions. It basically says this:

and

However, the distributive property does NOT work when the variables inside the parentheses are being multiplied or divided.

and

Let’s go through an example very carefully:

By applying the distributive property, we can multiply each term inside the parentheses by 4. This is called “distributing”.

Since 12x and 4 are not like terms, this is as far as we can go with the problem.

Well, what about subtraction? Let’s look at a subtraction problem using two different methods.

Factor : If any number be equal to the product of two more numbers, each of the latter is called a factor of the former.

Thus, 3, 5 and 7 are the factors of 105,

∴ 105 = 3 × 5 × 7

Similarly, 3, a, b and x are the factors of 3abx, because 3abx = 3 × a × b × x.

Coefficient :

The number expressed in figures or symbol which stands before an algebraical quantity as a multiplier, is call its coefficient.

Thus, in 5abc, 5 is the coefficient of abc, 5a is the coefficient of bc and 5ab is the coefficient of c.

Like and Unlike terms :

Terms or simple expressions are said to be<> like when they do not differ at all or differ only in their numerical coefficients; otherwise they are called unlike. Thus, 3ax2y2 and 5ax2y5 are like terms, whereas 3ax2y5 and 5ax2y4 are unlike, similarly, abc, 5axbd, 7a2b8 and c2d8x are all unlike.