Please help me out with this question.
The product of two numbers that differ by one is equal to one,
Without finding the two numbers, determine the difference of their cubes.
Thank You in Advance
The two numbers differ by 1.
So if these two numbers are $\displaystyle x$ and $\displaystyle y$, then $\displaystyle x - y = 1$.
The difference of their cubes is given by
$\displaystyle x^3 - y^3 = (x - y)(x^2 + xy + y^2)$
$\displaystyle = 1(x^2 + xy + y^2)$
$\displaystyle = x^2 + xy + y^2$.