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Algebraic Formulae & Their Application

An equation is a statement that two algebraic expressions are equal. If an equation is satisfied by any value of the variable, then equation is said to be an identity.
  1. (a + b)2 = a2 + 2ab + b2 = (a – b)2 + 4ab
  2. (a – b)2 = a2 – 2ab + b2 = (a + b)2 – 4ab
  3. (a + b)2 + (a – b)2 = 2(a2 + b2)
  4. (a + b)2 – (a – b)2 = 4ab
  5. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
  6. (a + b + c + d)2 = a2 + b2 + c2 + d2 + 2a (b + c + d)+ 2b (c + d) + 2cd
  7. (a + b) (a – b) = a2 – b2
  8. (x + a) (x + b) = x2 + (a + b) x + ab
  9. (x + a) (x + b) (x + c) = x3 + (a + b + c)x2 + (ab + bc + ca) x + abc
  10. (a + b)3 = a3 + 3ab (a + b) + b3
  11. (a – b)3 = a3 – 3ab (a – b) – b3
  12. a3 + b3 = (a + b)3 – 3ab (a + b)= (a + b) (a2 – ab + b2)
  13. a3 – b3 = (a – b)3 + 3ab (a – b) = (a – b) (a2 + ab + b2)
  14. a3 + b3 + c3 – 3abc = (a + b + c) (a2 + b2 + c2 – ab – ac – bc)
If a + b + c = 0 then a3 + b3 + c3 = 3abc




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