# Free Study Material For RRB Examination: Mathematics (Simplification)

## Free Study Material For RRB Examination

Subject : Mathematics (Simplification)

In simplification of an expression there are certain laws which should be strictly adhered to. These laws are as follows:

**‘VBODMAS’ Rule**

This rule gives the correct sequence in which the mathematical operation are to be executed so as to find out the value of a given expression.

Here, ‘V’ stands for Vicnaculum (or Bar), ‘B’ stands for ‘Bracket’, ‘O’ stands for ‘Of’, ‘D’ stands for ‘Division’, ‘M’ stands for ‘Multiplication’, ‘A’ stands for ‘Addition’ and ‘S’ stand for ‘Subtraction’.

(a) Here, ‘VBODMAS’ gives the order of simplification. Thus, the order of
performing the mathematical operations in a given expression are

**First : **Virnaculum or line bracket or bar

**Second: **Bracket

**Third: **Of

**Fourth: **Division

**Fifth: **Multiplication

**Sixth: **Addition &

**Seventh: **Subtraction

The above order should strictly be followed.

(b) There are four types of brackets.

(i) Square brackets [ ]

(ii) Curly brackets { }

(iii) Circular brackets ( )

(iv) Bar or Virnaculum –

Thus, in simplifying an expression all the brackets must be removed in the order ‘–’, ‘( )’, ‘{ }’ and ‘[ ]’.

## Modulus of a Real Number

The modulus of a real number x is defined as

= x, if a > 0

|x|

= x, if a < 0

## Basic Formulae

(i) (a + b)^{2} = a^{2} + 2ab + b^{2}

(ii) (a – b)2 = a2 – 2ab + b^{2}

(iii) (a + b)^{2} – (a – b)^{2} = 4ab

(iv) (a + b)^{2} + (a – b)^{2} = 2(a^{2} + b^{2})

(v) (a^{2} – b^{2}) = (a + b) (a – b)

(vi) (a + b + c)^{2} = a^{2} + b^{2} + c^{2} +
2(ab + bc + ca)

(vii) (a^{3} + b^{3}) = (a + b) (a^{2} – ab + b^{2})

(viii) (a^{3} – b^{3}) = (a – b) (a^{2} + ab + b^{2})

(ix) (a^{3} + b^{3} + c^{3} – 3abc) = (a + b + c), (a^{2}
+ b^{2} + c^{2} – ab – bc – ca)

(x) a^{3} + b^{3} + c^{3} = 3abc, if a + b + c = 0

**Example 1: **Simplify 1005 + 500 – 10 – 80.

**Solution. **1005 + 500 – 10 – 80 = 1005 + 490 – 80 = 1495 – 80 = 1415

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