a cube plus b cube explained visually

teachersofindia 1,266 views 17 slides Jun 20, 2018
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About This Presentation

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


Slide Content

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

a 3 + b 3 a a a b b b

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

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

rearranging pieces a 3 + b 3 a a – b a

rearranging pieces a 3 + b 3 a a – b a a + b b

rearranging pieces a 3 + b 3 a a – b a a + b b b

pieces rearranged a 3 + b 3 a a – b a a + b b b b

b ase area

b ase area: a 2 a 2 a a

b ase area: a 2 a - b a b

b ase area: a 2 – ab ab a - b a

b ase area: a 2 – ab a 2 – ab

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

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

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

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