Quant Formulae

Arithmatic Formulae:
  1. a^2-b^2 = (a+b)\times (a-b)
  2. a^2+b^2 = (a+b)^2-2ab=(a-b)^2+2ab
  3. (a+b)^2 = a^2+2ab+b^2 = (a-b)^2+4ab
  4. (a-b)^2 = a^2-2ab+b^2 = (a+b)^2-4ab
  5. a^3+b^3 = (a+b) \times (a^2-ab+b^2) = (a+b)^3-3ab \times (a+b)
  6. a^3-b^3 = (a-b) \times (a^2+ab+b^2) = (a-b)^3+3ab \times (a-b)
  7. (a+b)^3 = a^3+3a^2b+3ab^2+b^3 = a^3+b^3+3ab \times (a+b)
  8. (a-b)^3 = a^3-3a^2b+3ab^2-b^3 = a^3-b^3-3ab \times (a+b)
  9. (x+a) \times (x+b) = x^2+x \times (a+b)+ab
  10. (x-a) \times (x+b) = x^2+x \times (b-a)-ab
  11. (x-a) \times (x-b) = x^2-x \times (a+b)+ab
  12. (a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ac
  13. (a+b+c)^3 = a^3+b^3+c^3+3(a+b)(b+c)(c+a)
  14. a^4-b^4 = (a-b) \times (a+b) \times (a^2+b^2)
  15. a^6-b^6 = (a+b) \times (a^2-ab+b^2) \times (a-b) \times (a^2+ab+b^2)
  16. a^6+b^6 = (a^2+b^2) \times (a^4-a^2b^2+b^4)
  17. a^4+a^2b^2+b^4 = (a^2-ab+b^2) \times (a^2+ab+b^2)
  18. (a-b-c)^2 = a^2+b^2+c^2-2ab+2bc-2ac
  19. a^3+b^3+c^3-3abc = (a+b+c) \times (a^2+b^2+c^2-ab-bc-ac)
Indices Formulas:
The formulas involving relations between variables and their powers or powers and indices are:
  1. x^m \times x^n = x^{m+n}
  2. x^m \times x^n \times \ldots \times x^p = x^{m+n+ \ldots +p}
  3. x^m \div x^n = x^{m-n}
  4. x^m \div x^n \div \ldots \div x^p = x^{m-n- \ldots -p}
  5. (x^m)^n = x^{m \times n}
  6. ((x^m)^n)^o) = x^{m \times n \times o}
  7. x^0 = 1
  8. x^{-m} = \dfrac{1}{x^m}
  9. x^{m} = \dfrac{1}{x^{-m}}
  10. x^{\frac{m}{n}} = \sqrt[n]{x^m}
  11. \left( \dfrac{x^a}{y^b} \right)^c = \dfrac{x^{ac}}{y^{bc}}
  12. \dfrac{x^m}{y^m} = \left( \dfrac{x}{y} \right)^m
  13. \sqrt[m]{\dfrac{x^a}{y^b}} = \dfrac{x^{\frac{a}{m}}}{y^{\frac{b}{m}}}
  14. x^{\frac{p}{q}} = \sqrt[q]{x^p} = \left(\sqrt[q]{x}\right)^p
  15. \sqrt[m]{\dfrac{x}{y}} = \dfrac{\sqrt[m]{x}}{\sqrt[m]{y}}
  16. \sqrt{a} \times \sqrt {b} = \sqrt{a \times b}    provided that a , b and a*b are not negative numbers.
If, a^x = a^y then , x=y. ( Provided That : 0 < a\text{ and }a \ne 1 )
If, a^x = b^x then , a=b.  ( Provided That : 0 < a , b \text{ and }a , b \ne 1 )

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