Algebra all Formulas

Algebra Formulas

Square Identities

1. \( (a + b)^2 = a^2 + 2ab + b^2 \)

2. \( (a - b)^2 = a^2 - 2ab + b^2 \)

3. \( a^2 + b^2 = (a + b)^2 - 2ab \)

4. \( a^2 + b^2 = (a - b)^2 + 2ab \)

5. \( (a + b)^2 = (a - b)^2 + 4ab \)

6. \( (a - b)^2 = (a + b)^2 - 4ab \)

7. \( (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca \)

Cube Identities

8. \( (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 \)

9. \( (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 \)

10. \( (a + b)^3 = a^3 + b^3 + 3ab(a + b) \)

11. \( (a - b)^3 = a^3 - b^3 - 3ab(a - b) \)

Sum and Difference of Cubes

12. \( a^3 + b^3 = (a + b)(a^2 - ab + b^2) \)

13. \( a^3 - b^3 = (a - b)(a^2 + ab + b^2) \)

14. \( a^3 + b^3 = (a + b)^3 - 3ab(a + b) \)

15. \( a^3 - b^3 = (a - b)^3 + 3ab(a - b) \)

Special Identities

16. \( a^2 - b^2 = (a + b)(a - b) \)

17. \( a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca) \)

18. If \( a + b + c = 0 \), then \( a^3 + b^3 + c^3 = 3abc \)

19. \( a^2 + b^2 + c^2 - ab - bc - ca = \frac{1}{2}[(a - b)^2 + (b - c)^2 + (c - a)^2] \)