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SIMPLIFICATION

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

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

First: Vinculum or line bracket or bar, Second: Bracket, Third: Of, Fourth: Division

Fifth: Multiplication, Sixth: Addition &, Seventh: Subtraction

The above order should strictly be followed.

(2) There are four types of brackets.

Square brackets “[ ]”, Curly brackets “{ }”, Circular brackets “( )”, Bar or Vinculum “–“

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 = a2 + 2ab + b2

(ii) (a – b)2 = a2 – 2ab + b2

(iii) (a + b)2 – (a – b)2 = 4ab

(iv) (a + b)2 + (a – b)2 = 2(a2 + b2)

(v) (a2 – b2) = (a + b) (a – b)

(vi) (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

(vii) (a3 + b3) = (a + b) (a2 – ab + b2)

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