a cube plus b cube explained visually

Swati Sircar invites you to explore the cubic identities a^3 + b^3 through models.

1. a 3 + b 3 By Swati Sircar (longer version)

2. a 3 + b 3 a a a b b b

3. a 3 + b 3 b b b a a - b a b b a - b

4. a 3 + b 3 rearranging pieces (a – b)a 2 (a – b)ab ab 2 b 3

5. rearranging pieces a 3 + b 3 a a – b a

6. rearranging pieces a 3 + b 3 a a – b a a + b b

7. rearranging pieces a 3 + b 3 a a – b a a + b b b

8. pieces rearranged a 3 + b 3 a a – b a a + b b b b

9. b ase area

10. b ase area: a 2 a 2 a a

11. b ase area: a 2 a - b a b

12. b ase area: a 2 – ab ab a - b a

13. b ase area: a 2 – ab a 2 – ab

14. b ase area: a 2 – ab + b 2 a 2 – ab b 2

15. b ase area: a 2 – ab + b 2 h eight: a + b (a + b)(a 2 – ab + b 2 ) = a 3 + b 3 a 2 – ab b 2 a + b

16. model (a – b)a 2 (a – b)ab ab 2 b 3 a 3

17. Original model – VASCSC Model modified in 2014 with few extra blocks Model can be flattened out Shot at APU