Two Cubes

Strategies and Hints

  1. The volumes of the two cubes are x3 and y3. The figure models the binomial
    x    3 + y3.

  2. The three prisms described in the second hint are shown below.

  3. The volume of the light gray prism is y2(x + y).
    The volume of the dark gray prism is xy(x - y).
    The volume of the white prism is x2(x - y).

  4. x3 + y3 = y2(x + y) + xy(x - y) + x2(x - y)

 

Solution

So, x3 + y3 can be factored as (x + y)(x2 - xy + y2).