WOLFRAM|DEMONSTRATIONS PROJECT

Binomial Cube

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a
1
b
2
show labels
3
a
monomial
3
b
monomial
2
a
b monomials
2
b
a monomials
The cube of a binomial is the sum of four terms: the two cubes, three times the square of the first times the second, and three times the square of the second times the first. In symbols,
3
(a+b)
=
3
a
+
3
b
+3
2
a
b+3a
2
b
. This Demonstration shows the decomposition of the volume of a binomial cube into each one of its terms and these in turn into unit cubes.