a cube plus b cube plus c cube minus 3 a b c formula and a minus b whole square in terms of a plus b square and vice versa

\[a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ac) \]

 \[a^3+b^3+c^3-3abc=(a+b+c)\frac{1}{2}[(a-b)^2+(b-c)^2+(c-a)^2] \]

\[(a+b)^2= (a-b)^2+4ab \]

\[(a-b)^2= (a+b)^2-4ab \]

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