User shows that for any complex numbers $z₁, z₂∈ℂ$ and any positive integer $n$, we have the following: $z₁ⁿ⁻¹-z₂ⁿ⁻¹=z₁(z₁ⁿ-z₂ⁿ)(z₁-z₂)z₂ⁿ$