# Math Help - Problem Solving

1. ## Problem Solving

The product of two numbers that differ by one is equal to one,
Without finding the two numbers, determine the difference of their cubes.

2. Originally Posted by Martin Billado

The product of two numbers that differ by one is equal to one,
Without finding the two numbers, determine the difference of their cubes.

The two numbers differ by 1.

So if these two numbers are $x$ and $y$, then $x - y = 1$.

The difference of their cubes is given by

$x^3 - y^3 = (x - y)(x^2 + xy + y^2)$

$= 1(x^2 + xy + y^2)$

$= x^2 + xy + y^2$.