IMPORTANT MATHS FORMULAE

                  Algebra

1. (a + b)² = a² + 2ab + b²

2. (a – b)²  = a² – 2ab + b²

3. (a + b) (a – b) = a² – b²

4. (x + a)(x + b)  = x² + (a + b)x + ab

5. (x + a)(x – b)  = x² + (a – b)x – ab

6. (x – a)(x + b)  = x² + (b – a)x – ab

7. (x – a)(x – b)  = x²  – (a + b)x + ab

8. (a + b)³  = a³ + b³ + 3ab(a + b)

9. (a – b)³  =  a³ – b³ – 3ab(a – b)

10. (x + y + z) ²  = x² + y² + z² + 2xy + 2yz + 2xz

11. (x + y – z) ²  =  x² + y² + z² + 2xy – 2yz – 2xz

12. (x – y + z)²  = x² + y² + z² – 2xy – 2yz + 2xz

13. (x – y – z)²  = x² + y² + z² – 2xy +  2yz – 2xz

14. x³ + y³ + z³ – 3xyz  = (x + y + z)(x² + y² + z² – xy – yz -xz)

15. x² + y²  = 1212 [(x + y)² + (x – y)²]

16. (x + a) (x + b) (x + c) = x³ + (a + b +c)x² + (ab + bc + ca)x + abc

17. x³ + y³ = (x + y) (x² – xy + y²)

18. x³ – y³  = (x – y) (x² + xy + y²)

19. x² + y² + z² -xy – yz – zx = 1212 [(x-y)² + (y-z)² + (z-x)²]

Powers:
a^mxaⁿ  = a^m+n
aman=am−naman=am−n
(a^m)ⁿ  =  a^mn
(a^mbⁿ)^p =   a^mpb ^np
a^-m = 1am1am
amn=am−−−√namn=amn
Rules of Zero:
a¹  = a
a⁰ = 1
a*0 = 0
a is undefined
Linear Equation:
Linear equation in one variable ax + b = 0, x = – −ba−ba
Quadratic Equation:  ax² + bx + c  = 0  x  = −b±b2−4ac√2a−b±b2−4ac2a
Discriminant D = b² – 4ac
Math Formulas:
When rate of discount is given Discount =   MP∗Rate of Discount 100
Simple Interest = PTR100PTR100 where P = Principal, T = Time in years R = Rate of interest per annum
Principal = 100∗S.IR∗T100∗S.IR∗T
Rate = 100∗S.IP∗T100∗S.IP∗T
Time = 100∗S.IP∗R100∗S.IP∗R
Principal = Amount – Simple Interest
Discount = MP – SP
Trigonometry:


Probability
P(E) =   Number of outcomes favorable to E
Total Number of Possible Outcomes

Mensuration