Toolkit 12

Sum of cubes (factored)

a^3+b^3=(a+b)(a^2-ab+b^2)

Proof

Using the distributive law,

\begin{aligned} (a+b)(a^2 - ab + b^2) &= a^3 - a^2b + ab^2 + a^2b - ab^2 + b^3 \\ &= a^3 + b^3. \quad\square \end{aligned}