simplification Topic-wise Short Notes, Solutions, Methods, Tips, Tricks & Techniques to Solve Problems

Simplification - Basic Formulas, Shortcuts, Rules, Tricks & Tips - Quantitative Aptitude

Useful For All Competitive Exams Like UPSC, SSC, BANK & RAILWAY

Posted By Careericons Team

Introduction to Simplification:

Simplification basically means finding an answer for a complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus.

To simplify a given expression accurately, the magic word is VBODMAS. In a lengthy and complicated algebraic expression, start from the left and apply VBODMAS in the same order as it appears in the term.

This rule depicts the correct sequence in which the operations are to be executed, so as to find out the value of a given expression, Where

We first remove the bar and then brackets n the order parenthesis ( ), then curly brackets { }, then the square bracket [ ]. Then we proceed with the arithmetic operations of division, multiplication, addition and subtraction in that order.

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Top 20 Basic Arithmetic Formulas Useful To Solve All Simplification & Rationalising Surds Problems

In this types of simplification problems you need to solve . There are few basic formulas which helps in finding the solutions for the given questions.

Remember the following arithmetic formulas:

1. $(a + b)^2 = a^2 + b^2 + 2ab$
2. $(a – b)^2 = a^2 + b^2 – 2ab$
3. $(a + b)^2 = (a – b)^2 + 4ab$
   or
   $(a + b)^2 – (a – b)^2 = 4ab$
4. $(a + b)^2 = 2(a^2 + b^2 ) – (a – b)^2$
   or
   $(a + b)^2 + (a – b)^2 = 2(a^2 + b^2)$
5. $a^2 + b^2 = (a + b)^2 – 2ab$
   or
   $a^2 + b^2 = (a – b)^2 + 2ab$
6. $a^2 – b^2 = (a + b) (a – b)$
7. $a^3 + b^3 = (a + b) (a^2 – ab + b^2)$
   or
   $a^3 + b^3 = (a + b)^3 – 3ab (a + b)$
8. $a^3 – b^3 = (a – b) (a^2 + ab + b^2)$
   or
   $a^3 – b^3 = (a – b)^3 + 3ab (a – b)$
9. $(a + b)^3 = a^3 + 3a^2b + 3ab^2 +b^3$
   or
   $(a + b)^3 = a^3 + b^3 + 3ab (a + b)$
10. $(a – b)^3 = a^3 – 3a^2b + 3ab^2 – b^3$
    or
    $(a – b)^3 = a^3 – b^3 – 3ab (a – b)$
11. $a^4 – b^4 = (a^2 + b^2 ) (a + b) (a – b)$
12. $(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$
13. $(a + b + c)^3 = a^3 + b^3 + c^3 + 3(b + c) (c + a) (a + b)$
14. $a^3 + b^3 + c^3 – 3abc = (a + b + c) (a^2 + b^2 + c^2 – ab – bc – ca)$
    or
    $a^3 + b^3 + c^3 – 3abc = 1/2 (a + b + c) [(a – b)^2 +(b–c)^2 +(c–a)^2 ]$
15. If $a + b + c = 0$, then $a^3 + b^3 + c^3 = 3abc$
16. $a + b + c = {a^3 + b^3 + c^3 - 3abc}/{a^2 + b^2 + c^2 - ab - bc -ca}$
17. $(a + b) (b + c) (c + a) = ab (a + b) + bc (c + b) + ca (c + a) + 2abc$
18. $(a – b) (b – c) (c – a) = –[a^2 (b – c) + b^2 (c – a) + c^2 (a – b)]$
19. $(a + b + c) (ab + bc + ca) = a^2 (b + c) + b^2 (c + a) + c^2 (a + b) +3abc$
20. $(x + a) (x + b) = x^2 + x (a + b) + ab$

By using these formulas you can find solutions for the simplification problems like,

1. To find a calculation is given and one of the numbers is missing from the calculation. To find out the missing number, we have to approximate the given numbers or do the basic operations.
2. To find all the numbers are given with some operations between them & we have to simplify the calculation.

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"16" - Important Aptitude Rules, Formulas & Quick Tricks to Solve Simplification Based Aptitude Problems

In this list of rules, you will get an idea that How to solve all different types & kinds of Simplification based aptitude problems asked in various competitive exams like UPSC, SSC, Bank, and Railway examinations at all levels.

By using this method, you can able to solve all problems from basic level to advanced level of questions asked based on Simplification in a faster approch.

Let's discuss the rules one by one with all Simplification related formulas with examples,

RULE 1 :

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

There are four types of brackets given below.

1. – → Line/Bar
2. ( ) → Simple or Small Bracket/open brackets
3. { } → Curly Brackets/Braces
4. [ ] → Square Brackets/Closed brackets

These brackets must be solved in given order only.

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RULE 2 :

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RULE 3 :

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RULE 4 :

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RULE 5 :

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RULE 6 :

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RULE 7 :

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RULE 8 :

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Refer: Get all Topic-wsie Quantitative aptitude problems for upcoming competitiveexams