বীজগাণিতিক সূত্র

বীজগাণিতিক সূত্র:

(a + b)² = a² + 2ab + b²

(a + b)² = (a – b)² + 4ab

(a – b)² = a² – 2ab + b²
(a – b)² = (a + b)² – 4ab

a² + b² = (a + b)² – 2ab

a2 + b2 = (a – b)² + 2ab

a² – b² = (a + b) – (a – b)

2 (a² +b²) = (a + b)² + (a – b)²

(a + b + c)² = (a² + b² + c²) + 2 (ab + bc + ca)

(a² + b² + c²) = (a + b + c)² – 2(ab + bc + ca)

2 (ab + bc + ca) = (a + b + c)² – (a² + b² + c²)

(a + b)³= a³ + 3a²b + 3ab² + b³

(a + b) ³= a³ + b³ + 3ab (a + b)

(a – b) ³= a³ – 3a²b + 3ab² – b3

(a – b) ³= a³ – b³ – 3ab (a – b)

a³ + b³ = (a + b) (a² – ab + b²)

a³ + b³ = (a + b) ³– 3ab (a + b)

a³ – b³ = (a – b) (a² + ab + b²)

a³ – b³ = (a – b) ³+ 3ab (a – b)

(a + b + c) ³= a³ + b³ + c³ + 3 (a + b) (b + c) (c + a)

a³ + b³+ c³ – 3abc = (a + b + c) (a² + b² + c² – ab – bc – ca)

a3 + b3 + c3 – 3abc = (a + b + c) { (a – b)² + (b – c)² + (c – a)²}

4ab = (a + b)² – (a – b)²

(x + a) (x + b) = x² + (a + b) x + ab

(x + a) (x – b) = x² + (a – b) x – ab

(x – a) (x + b) = x² + (b – a) x – ab

(x – a) (x – b) = x² – (a + b) x + ab

(x + p) (x + q) (x + r) = x³ + (p + q + r) x² + (pq + qr + rp) x +pqr

bc (b – c) + ca (c – a) + ab (a – b) = – (b – c) (c – a) (a – b)

a²(b – c) + b²(c – a) + c²(a – b) = – (b – c) (c – a) (a – b)

a(b² – c²) + b (c² – a²) + c (a² – b²) = (b – c) (c – a) (a – b)

a³ (b – c) + b³ (c – a) + c³ (a – b) = – (b – c) (c – a) (a – b) (a + b + c)

b²c²(b² –c²) +c²a²(c² –a²) + a²b²(a² –b²) = – (b–c) (c–a) (a–b) (b+c) (c+a) (a+b)

(ab + bc + ca) (a + b + c) – abc = (a + b) (b + c) (c + a)

(b + c) (c + a) (a + b) + abc = (a + b +c) (ab + bc + ca)