# Simplification Rules

Importance : 1 or 2 questions based on simplification are essential part of almost every competitive exams. The difficulty level varies based on examination level.

Scope of questions : The mostly asked questions are based on complex, fractions, decimal, squares, cubes, square roots and cube roots. Questions are completely numerical kind with no alongways.

Way to success : Note that BODMAS rule and other simplification TRICKS & RULES are completely followed. Your concentration and ‘Mental calculation’ will help most in these questions.

Rules 1 :  An expression must be simplified by following defined order/sequence known as VBODMAS, which is given by :

1st step , V – Vineculum(line brackets)/ Bar

B – Brackets

O – Of

D – Division

M – Multiplication

Last Step, S – Subtraction

There are four types of brackets given below.

(i) – → Line/Bar

(ii) ( ) → Simple or Small Bracket/open brackets

(iii) { } → Curly Brackets/Braces

(iv) [ ] → Square Brackets/ Closed brackets

These brackets must be solved in given order only.

Rule 2:

$$\frac { 1 }{ n\left( n+1 \right) } +\frac { 1 }{ \left( n+1 \right) \left( n+2 \right) } +\frac { 1 }{ \left( n+2 \right) \left( n+3 \right) } ….+\frac { 1 }{ \left( n+r-1 \right) \left( n+r \right) }$$

$$=\quad \left( \frac { 1 }{ n } -\frac { 1 }{ n+1 } \right) +\left( \frac { 1 }{ n+1 } -\frac { 1 }{ n+2 } \right) +\left( \frac { 1 }{ n+2 } -\frac { 1 }{ n+3 } \right)$$

$$+……+\left( \frac { 1 }{ n+r-1 } -\frac { 1 }{ n+r } \right) =\left( \frac { 1 }{ n } -\frac { 1 }{ n+r } \right)$$

Rule 3 :

$$\frac { 1 }{ n\left( n+2 \right) } +\frac { 1 }{ \left( n+2 \right) \left( n+4 \right) } +\frac { 1 }{ \left( n+4 \right) \left( n+6 \right) }$$

$$+….+\frac { 1 }{ \left( n+2r-2 \right) \left( n+2r \right) } =\frac { 1 }{ 2 } \left( \frac { 1 }{ n } -\frac { 1 }{ n+2r } \right)$$

Rule 4 :

$$FORMULA→\frac { { a }^{ 3 }+{ b }^{ 3 } }{ { a }^{ 2 }-ab+{ b }^{ 2 } }$$

$$=(a+b)$$

Rule 5 :

$$FORMULA→\frac { { a }^{ 3 }-{ b }^{ 3 } }{ { a }^{ 2 }+ab+{ b }^{ 2 } }$$

$$=(a-b)$$

Rule 6 :

$$FORMULA→\frac { { \left( a+b \right) }^{ 2 }+{ \left( a-b \right) }^{ 2 } }{ \left( { a }^{ 2 }+{ b }^{ 2 } \right) } =2$$

Rule 7 :

$$FORMULA→{ a }^{ 2 }+2ab+{ b }^{ 2 }={ \left( a+b \right) }^{ 2 }$$

Rule 8 :

$$\frac { { a }^{ 2 }-{ b }^{ 2 } }{ a-b } =a+b\quad or,\quad \frac { { a }^{ 2 }-{ b }^{ 2 } }{ a+b } =a-b$$

Basic Formula :

Read Formula on Simplification Formulas | SSC,IBPS,BANK,ARMY,GOVT EXAM

Some Other Formulas are given below.

$$1.\quad { a }^{ 2 }+\frac { 1 }{ { a }^{ 2 } } ={ \left( a+\frac { 1 }{ a } \right) }^{ 2 }-2={ \left( a-\frac { 1 }{ a } \right) }^{ 2 }+2$$

$$2.\quad { \left( a+\frac { 1 }{ a } \right) }^{ 3 }={ a }^{ 3 }+\frac { 1 }{ { a }^{ 3 } } +3\times \left( a+\frac { 1 }{ a } \right)$$

$$3.\quad { \left( a-\frac { 1 }{ a } \right) }^{ 3 }={ a }^{ 3 }-\frac { 1 }{ { a }^{ 3 } } -3\times \left( a-\frac { 1 }{ a } \right)$$

Thanks you and All the best!

For always keep in touch with updates you can join or visit at Facebook Page  or Twitter

Square Root and Cube Root

Simplification Important Questions For SSC CGL 2018

Updated: January 8, 2018 — 8:36 am