Formula for Algebra

বীজ গণিতের সুত্রঃ

1. (a+b)²= a²+2ab+b²
2. (a+b)²= (a-b)²+4ab
3. (a-b)²= a²-2ab+b²
4. (a-b)²= (a+b)²-4ab
5. a² + b²= (a+b)²-2ab.
6.a² + b²= (a-b)²+2ab.
7. a²-b²= (a +b)(a -b)
8. 2(a²+b²)= (a+b)²+(a-b)²

🏅(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 }
🏅(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

9. 4ab = (a+b)²-(a-b)²
10. ab = {(a+b)/2}²-{(a-b)/2}²
11. (a+b+c)² = a²+b²+c²+2(ab+bc+ca)
12. (a+b)³ = a³+3a²b+3ab²+b³
13. (a+b)³ = a³+b³+3ab(a+b)
14. a-b)³= a³-3a²b+3ab²- b³
15.(a-b)³= a³-b³-3ab(a-b)
16. a³+b³= (a+b) (a²-ab+b²)
17. a³+b³= (a+b)³-3ab(a+b)
18. a³-b³ = (a-b) (a²+ab+b²)
19. a³-b³ = (a-b)³+3ab(a-b)