Question

verify a3+b3=(a+b)(a2-ab+b2) by an activity.

Answer 1

We can do geometrical demonstration by using cubes and cuboids.

see the diagram.

Dimensions of cuboids:

 

Blue cuboid:  a    a   b

Rose cube:     a   a   a

Gold cuboid:  a  b  b

Green cube :   b  b  b

 

Blue cuboid + Rose cube together:   (a+b) a   a

Gold cuboid + Green cube together : (a+b) b b

Blue + Rose + Gold + Green   =  (a+b) a a + (a+b) b b

   = a a a + b a a + a b b + b b b = rose + blue + Gold + Green

   = a³ + (Blue + Gold ) + b³

    = a³ +  (a+b) a b    + b³

So  (a+b) a a + (a+b) b b = a³ + (a+b) a b + b³

       (a+b) (a² + b²) = a³ + (a+b) a b + b³

       (a+b) (a² + b²) -  (a+b) a b = a³ + b³

       (a+b) (a² - ab + b²) = a³ + b³