Algebra Formula – बीजगणित सूत्र

बीजगणित सूत्र (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)(a^n-1 + a^n-2 +…+ b^n-2a + b^n-1)
• सम संख्या (Even) –  (n = 2k), aⁿ + bⁿ = (a + b)(a^n-1 – a^n-2b +…+ b^n-2a – b^n-1)
• विषम संख्या (Odd) – (n = 2k + 1), aⁿ + bⁿ = (a + b)(a^n-1 – a^n-2b +…- b^n-2a + b^n-1)
• (a + b + c + …)² = a² + b² + c² + … + 2(ab + ac + bc + ….

• घातांक के नियम (Low Of Formula Exponents)
  1. (a^m)(aⁿ) = a^m+n
  2. (ab)^m = a^mb^m
  3. (a^m)ⁿ = a^mn
• (आंशिक घातांक) Fractional Exponents
  1. a⁰ = 1
  2. aman=am−naman=am−n
  3. amam = 1a−m1a−m
  4. a−ma−m = 1am