# SSC Quantitative Aptitude tricks: Algebraic formulae & their applications

In this article, we will learn about all algebraic formulas and their applications with shortcut tricks because all questions are based on algebraic formulas.  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.

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

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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;

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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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