নবম-দশম শ্রেণির গণিতের বীজগণিত এবং ত্রিকোনোমিতির যাবতীয় সূত্রাবলি

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(α² + в²) = (a + в)² + (a – в)²

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) a³ + b³ = (a + b) (a² – ab + b²)

16) a³ + b³ = (a + b)³ – 3ab (a + b)

17) a³ -b³ = (a – b) (a² + ab + b²)

(18) a³ – b³ = (a – b)³ + 3ab (a – b)

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

1. sin(A + B) = sinA.cosB + cisA.sinB
2. sin(A - B) = sinA.cosB - cisA.sinB
3. cos(A + B) = cosA.cosB - sinA.sinB
4. cos(A - B) = cosA.cosB + sinA.sinB
5. tan(A + B) = ^{tanA + tanB}_{1 - tanA.tanB}
6. tan(A - B) = ^{tanA - tanB}_{1 + tanA.tanB}
7. cot(A + B) = ^{cotA.cotB - 1}_{cotA + cotB}
8. cot(A - B) = ^{cotA.cotB + 1}cotB - cotA
   
9. sin(A + B).sin(A - B) = sin²A - sin²B = cos²B - cos²A

cos(A + B).cos(A - B) = cos²A - sin²B = cos²B - sin²A