Difference of Two Powers/Examples/Difference of Two Cubes/Corollary

Theorem

$x^3 - 1 = \paren {x - 1} \paren {x^2 + x + 1}$

Proof

From Difference of Two Cubes:

$x^3 - y^3 = \paren {x - y} \paren {x^2 + x y + y^2}$

The result follows directly by setting $y = 1$.

$\blacksquare$

Sources

• 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 3$. Roots of Unity: $(3.5)$