#Maths Formulae for General competitions (Written by NM Mishra on the behalf of Brilliant Academy of Learning on 08/05/2020)#

   Important Maths Formulae for General competitions & Entrance Exams

1. (a+b)2=a2+2ab+b2

[a plus b whole square is equal to a square plus two a b  plus b square]

2.(a+b)2=(a-b)2+4ab

[a plus b whole square is equal to a minus b whole square plus four a b ]

3.(a-b)2=a2-2ab+b2

[a minus b whole square is equal to a square minus two a b plus b square]

4.(a-b)2=(a+b)2-4ab

[a minus b whole square is equal to a plus b whole square minus four a b]

5. a2-b2=(a+b)(a-b)

[a square minus b square is equal to a plus b multiplied by a minus b]

6. (a+b)2+(a-b)2=2(a2+b2)

[a plus b whole square plus a minus b whole square is equal to two multiplied in sum of a square and b square]

7. (a+b)2- (a-b)2=4ab

[a plus b whole square minus a minus b whole square is equal to four a b ]

8.(a+b+c)2=a2+b2+c2+2ab+2bc+2ca

[a plus b plus c whole square is equal to a square plus b square plus c square plus two a b plus two b c plus two c a ]

9.(a+b)3=a3+b3+3ab(a+b)

[a plus b whole cube is equal to a cube plus b cube  plus three a b multiplied by sum of a and b]

10.(a-b)3=a3-b3-3ab(a-b)

[a minus b whole cube is equal to a cube minus b cube minus three a b multiplied by difference of a minus b ]

11.a3+b3=(a+b)(a2-ab+b2)

[a cube plus b cube is equal to a plus b multiplied by a square minus a b plus b square]

12. a3-b3=(a-b)(a2+ab+b2)

[a cube minus b cube is equal to a minus b multiplied by a square plus a b plus b square]

13.a3+b3+c3-3abc =(a+b+c)(a2+b2+c2-ab-bc-ca)

[a cube plus b cube plus c cube minus three a b c  is equal to a plus b plus c multiplied by a square plus b square plus c square minus a b minus b c minus c a ]

14. a3+b3+c3-3abc=1/2(a+b+c)[(a-b)2+(b-c)2+(c-a)2]

[a cube plus b cube plus c cube minus three a b c is equal to half a plus b plus c multiplied by sum of a minus b whole square plus b minus c whole square plus c minus a whole square]

Sum for Arithmetic Series

s=Sum of terms

n=number of terms

a=First term

l =Last term

d = common difference between two succeeding terms

nth term =last term 

15. 1+2+3+4+................+n= n/2(n+1)

16. 1+3+5+7+...............+n= n2

17.  2+4+6+8+..............+n=n(n+1)

18.  S = n/2(a+l)

19. S=n/2[2a+(n-1)d]

20.  1^2+2^2+3^2+..............+n^2 = n(n+1)(2n+1)/6

21. 1^3+2^3+3^3+...........+n^3= [n(n+1)/2]^2

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