Geometric Representation of the Cube of a Sum

a

1.4

opacity

0.5

blocks

3

a

3

b

2

a

b

2

a

b

2

a

b

a

2

b

a

2

b

a

2

b

This Demonstration shows a geometric analog of the formula

3

(a+b)

=

3

a

+3

2

a

b+3a

2

b

+

3

b

. This is done by dissecting a cube with side length

a+b

into eight solids: two cubes with side lengths

a

and

b

,

three congruent rectangular solids with dimensions

a×a×b

and three rectangular solids with dimensions

a×b×b

.