Algebra Formula – बीजगणित सूत्र

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Algebra Formula

  • a2 – b2 = (a – b)(a + b)
  • (a+b)2 = a2 + 2ab + b2
  • a2 + b2 = (a – b)2 + 2ab
  • (a – b)2 = a2 – 2ab + b2
  • (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
  • (a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
  • (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
  • (a – b)3 = a3 – 3a2b + 3ab2 – b3
  • a3 – b3 = (a – b)(a2 + ab + b2)
  • a3 + b3 = (a + b)(a2 – ab + b2)
  • (a + b)3 = a3 + 3a2b + 3ab2 + b3
  • (a – b)3 = a3 – 3a2b + 3ab2 – b3
  • (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
  • (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
  • a4 – b4 = (a – b)(a + b)(a2 + b2)
  • a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
  • प्राकृतिक संख्या (Natural Numbers) – an – bn = (a – b)(an-1 + an-2 +…+ bn-2a + bn-1)
  • सम संख्या (Even) –  (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
  • विषम संख्या (Odd) – (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)
  • (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….
  • घातांक के नियम (Low Of Formula Exponents)
    1.
    (am)(an) = am+n
    2. (ab)m = ambm
    3. (am)n = amn
  • (आंशिक घातांक) Fractional Exponents

Maths Formulas PDF Download

Exponent Law

  • √a = a 1/2

  • ∛a = a 1/3
  • √a = a 1/n
  • p.  a = a p + q
  • / a  = a p – q
  • p.  b = (ab) p
  • (a q.  = a pq
  •  = 1
  • –n.  = 1/a n

Important Algebra Formulas

Square Formulas

  • (a + b) = a + b + 2ab
  • (a − b) = a + b − 2ab
  • − b = (a − b) (a + b)
  • (x + a) (x + b) = x + (a + b) x + ab
  • (a + b + c) = a + b + c  + 2ab + 2bc + 2ca
  • (a + (−b) + (−c)) = a + (−b)  + (−c) + 2a (−b) + 2 (−b) (−c) + 2a (−c)(a – b – c) = a + b + c − 2ab + 2bc − 2ca

Cube Formulas

  • (a + b) = a + b + 3ab(a + b)
  • (a − b) = a – b – 3ab(a – b)
  • − b = (a − b) (a + b + ab)
  • + b = (a + b) (a + b − ab)
  • (a + b + c) = a + b + c + 3(a + b)(b + c)(c + a)
  • + b + c 3  − 3abc = (a + b + c) (a + b + c − ab − bc − ac)

Power n Formula

  • − b = (a − b) (a n−1 + a n−2   + a n−3  + …. + a 1  n−2  + b n−1  )
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