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SSC Quantitative Aptitude tricks: Algebraic formulae & their applications

Feb 5, 2018 14:25 IST
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ssc algebra tricks
ssc algebra tricks

Algebraic formulas play a very important role in solving aptitude questions related to various topics. It is estimated that 2-4 questions are always asked approximately in SSC exams from this section. The difficulty level of questions depends upon your adopted approach. Some questions consumes a lot of time in calculation because of their complexity.

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In this article, we will learn about all algebraic formulas and their applications with shortcut tricks because all questions are based on algebraic formulas. Let us take a tour of it.

Different Algebraic formulae

These formulas are not only important to solve questions for algebraic equations but also play a vital role in solving questions of Co-ordinate geometry, trigonometric functions, areas and perimeter and etc. these formulas are as follows-

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  1. a2 – b2 = (a – b)(a + b)
  2. (a + b)2 = a2 + 2ab + b2
  3. a2 + b2 = (a – b)2 + 2ab
  4. (a – b)2 = a2 – 2ab + b2
  5. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
  6. (a + b + c)3 = a3 + b3 + c3 + 3(a + b)(b + c)(c + a)
  7. a3 + b3 + c3- 3abc = (a + b+ c) (a2 + b2 + c2 - ab - ac - bc)
  8. (a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
  9. (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
  10. (a – b)3 = a3 – 3a2b + 3ab2 – b3
  11. a3 – b3 = (a – b)(a2 + ab + b2)
  12. a3 + b3 = (a + b)(a2 – ab + b2)
  13. (a + b)3 = a3 + 3a2b + 3ab2 + b3
  14. (a – b)3 = a3 – 3a2b + 3ab2 – b3
  15. (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
  16. (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
  17. a4 – b4 = (a – b)(a + b)(a2 + b2)
  18. a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
  19. if  a + b + c=0; then a3 + b3 + c3 =0
  20. x2+ x(a + b) + ab = (x + a) (x + b)
  21. ab (a + b) + bc (c + b) + ca (c + a) = (a + b)(b + c) (c + a)
  22. a2(b + c ) + b2 (c + a) + c2 (a + b)+ 3abc = (a + b + c) (ab + bc + ca)
  23. a2(b - c ) + b2 (c - a) + c2 (a - b) = (a – b)(b – c) (c – a)
  24. If n is a natural number, an – bn = (a – b)(an-1 + an-2b+…+ bn-2a + bn-1)
  25. If n is even (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
  26. If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)
  27. (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….
  28. Laws of Exponents         
    (am)(an) = am+n    
    (ab)m = ambm        
    (am)n = amn

 29. If a + b +c = abc, then

 

Important Points

  • You can learn these formulas only by applying them in the several questions.
  • Get the formula right because opting wrong formula can never land you to the right solution.

Questions

1. If a4 + b4 = a2b2, then (a6 + b6) equals to?

Ans.:-  Apply a3 + b3 = (a + b)(a2 – ab + b2) formula;

(a6 + b6) = (a2)3 + (b2)3

= (a2 + b2)( a4 + b4- a2b2)

= (a2 + b2)( a2b2- a2b2)

=0

2.

Ans.:- Replace 2.697 = x and 0.498 = y;

 

3.

 Ans:- Solution will proceed as follows-

 

4. The value of (x +y +z)3 - (y + z –x)3- (z + x –y)3- (x +y –z)3 is?

Ans.:- Simplify the above equation using (a + b + c)3= a3 + b3 + c3 + 3(a + b)(b + c)(c + a)

Above formula after simplification will look like this-

(a + b + c)3= a3 + b3 + c3 + 3a2b + 3ab2 + 3bc2 + 3b2c + 3a2c + 3ac2 + 6abc

Hence, (x +y +z)3 = x3 + y3 + z3 + 3x2y + 3xy2 + 3yz2 + 3y2z + 3x2z + 3xz2 + 6xyz --- (i)

(y + z –x)3=  -x3 + y3 + z3 + 3x2y - 3xy2 + 3yz2 + 3y2z + 3x2z - 3xz2 - 6xyz ------(ii)

(z + x –y)3= x3 - y3 + z3 - 3x2y + 3xy2 - 3yz2 + 3y2z + 3x2z + 3xz2 - 6xyz   -------(iii)

(x +y –z)3= x3 + y3 - z3 + 3x2y + 3xy2 + 3yz2 - 3y2z - 3x2z + 3xz2 - 6xyz  --------(iv)

Arrange the all four equations as per the question requirement-

= (x3 + y3 + z3 + 3x2y + 3xy2 + 3yz2 + 3y2z + 3x2z + 3xz2 + 6xyz)-( -x3 + y3 + z3 + 3x2y - 3xy2 + 3yz2 + 3y2z + 3x2z - 3xz2 - 6xyz)-( x3 - y3 + z3 - 3x2y + 3xy2 - 3yz2 + 3y2z + 3x2z + 3xz2 - 6xyz)-( x3 + y3 - z3 + 3x2y + 3xy2 + 3yz2 - 3y2z - 3x2z + 3xz2 - 6xyz)

=24xyz

The above-discussed problems are among the typical ones. Questions framed in SSC exams are generally based on the above formulas. This aptitude section requires a lot of practice to excel in the exams.

Keep on looking us for further tips and tricks in SSC quantitative aptitude question solving.

All the best!!

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