Alg1.2.8

From Exampleproblems

Simplify $(a^\frac{1}{3}+b^\frac{1}{3}+c^\frac{1}{3})(a^\frac{2}{3}-(a^\frac{1}{3})(b^\frac{1}{3}-(b^\frac{1}{3})(c^\frac{1}{3})-(c^\frac{1}{3})(a^\frac{1}{3})+b^\frac{2}{3}+c^\frac{2}{3})\,$

Applying the formula $(a^\frac{1}{3})^3+(b^\frac{1}{3})^3+(c^\frac{1}{3})^3-3(a^\frac{1}{3})(b^\frac{1}{3})(c^\frac{1}{3})\,$

Answer is $a+b+c-3(a^\frac{1}{3})(b^\frac{1}{3})(c^\frac{1}{3})\,$

$a+b+c-3(abc)^\frac{1}{3}\,$