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Algebraic Formula

Basic Algebraic Formula are listed below :

  • \((a+b)^{2} =a^{2}+2ab+b^{2}\)
  • \((a-b)^{2} =a^{2} - 2ab + b^{2} \)
  • \( (a+b)^{2} + (a-b)^{2} =2a^{2} + 2b^{2} \)
  • \( (a+b)^{2} -(a-b)^{2} = 4ab \)
  • \( a^{2} + b^{2} =(a+b)^{2} - 2ab \)
  • \( a^{2} + b^{2} = (a-b)^{2} + 2ab \)
  • \( a^{2} - b^{2} = (a-b)(a+b) \)
  • \( (a+b+c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc +2ca \)
  • \( (a-b+c)^{2} = a^{2} + b^{2} + c^{2} -2ab -2bc + 2ac \)
  • \( (a + b -c)^{2} = a^{2} + b^{2} + c^{2} + 2ab -2bc -2ac \)
  • \( (a+b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}\)
  • \( (a+b)^{3} = a^{3} + b^{3} + 3ab(a+b) \)
  • \( (a-b)^{3} = a^{3} - 3a^{2}b + 3ab^{2} - b^{3} \)
  • \( (a-b)^{3} = a^{3} - b^{3} -3ab(a-b) \)
  • \( a^{3} + b^{3} = (a+b)(a^{2} -ab +b^{2} \)
  • \( a^{3} + b^{3} = (a+b)^{3} - 3ab(a+b) \)
  • \( a^{3} - b^{3} = (a-b)(a^{2} + ab + b^{2})\)
  • \( a^{3} - b^{3} = (a - b)^{3} + 3ab(a-b) \)
  • \((a + b + c)(a^{2} + b^{2} + c^{2} -ab - bc - ca ) = a^{3} + b^{3} + c^{3} -3abc \)
  • If a + b + c = 0 then \( a^{3} + b^{3} + c^{3} = 3abc \)
  • \( a^{2} + b^{2 } + c^{2} - ab - bc - ca = \frac{1}{2} [(a-b)^{2} + (b-c)^{2} + (c-a)^{2}]\)
  • In Algebraic formula we have multiplication of binomials using FOIL METHOD: Which is as follows,
  • FOIL METHOD :
    F= First terms
    O = Outer terms
    I = Inner terms
    L = Last terms
    (a + b ) ( c + d) = ac + ad + bc + bd 
  • (x+a)(x+b)=\(x^{2}\)+(a+b)x+ab
  • \( (a + b)^{4} = a^{4} + 4a^{3}b+ 6a^{2}b^{2} + 4ab^{3} + b^{4}\)
  • \( (a- b)^{4} = a^{4} - 4a^{3}b + 6a^{2}b^{2}  - 4ab^{3} + b^{4} \)

These are some of Algebraic Formula given.

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