Properties of variables

Algebraic Expression of Class 7

Properties of variables with examples 

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

algebraic properties

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:

algebraic distributive property x(y+z)=xy+xz


What is variable

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

What is variable


What is variable

Let’s go through an example very carefully:

What is variable

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

What is variable

What is variable

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.

What is variable

What is variable

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.

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