# 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!

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Square Root and Cube Root

Simplification Important Questions For SSC CGL 2018

Updated: January 8, 2018 — 8:36 am