Factoring Differences Of Cubes The Formula. Explained With 3 ...

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We can verify the factoring formula by expanding the result and seeing that it simplifies to the original, as follows.

$$ \begin{align*} \blue{(a-b)}(a^2 + ab + b^2) & = a^2\blue{(a-b)} + ab\blue{(a-b)} + b^2\blue{(a-b)}\\ & = a^3 - a^2b + a^2b - ab^2 + ab^2 - b^3\\ & = a^3 \blue{- a^2b + a^2b}\,\,\red{ - ab^2 + ab^2} - b^3\\ & = a^3 + \blue 0 + \red 0 - b^3\\ & = a^3 - b^3 \end{align*} $$

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