# 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)