Algebra Formula – बीजगणित सूत्र

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Algebra Formula
Exponent Law

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+n2. (ab)^m = a^mb^m3. (a^m)ⁿ = a^mn
(आंशिक घातांक) Fractional Exponents
$\frac{1}{a^{m}}$

Maths Formulas PDF Download

Exponent Law

√a = a ^1/2
∛a = a ^1/3
ⁿ√a = a ^1/n
a ^p. a ^q= a ^{p + q}
a ^p/ a ^q = a ^{p – q}
a ^p. b ^p= (ab) ^p
(a ^p) ^q. = a ^pq
a ⁰^. = 1
a ^–n. = 1/a ⁿ

Important Algebra Formulas

Square Formulas (a + b) 2 = a 2 + b 2 + 2ab (a - b) 2 = a 2 + b 2 - 2ab a 2 - b 2 = (a - b) (a + b) (x + a) (x + b) = x 2 + (a + b) x + ab (a + b + c) 2 = a 2 + b 2 + c 2 + 2ab + 2bc + 2ca (a + (-b) + (-c)) 2 = a 2 + (-b) 2 + (-c) 2 + 2a (-b) + 2 (-b) (-c) + 2a (-c)(a - b - c) 2 = a 2 + b 2 + c 2 - 2ab + 2bc - 2ca Cube Formulas (a + b) 3 = a 3 + b 3 + 3ab(a + b) (a - b) 3 = a 3 - b 3 - 3ab(a - b) a 3 - b 3 = (a - b) (a 2 + b 2 + ab) a 3 + b 3 = (a + b) (a 2 + b 2 - ab) (a + b + c) 3 = a 3 + b 3 + c 3 + 3(a + b)(b + c)(c + a) a 3 + b 3 + c 3 - 3abc = (a + b + c) (a 2 + b 2 + c 2 - ab - bc - ac) Power n Formula a n - b n = (a - b) (a n-1 + a n-2 b 1 + a n-3 b 2 + \dots. + a 1 b n-2 + b n-1)