What is expand c^{1/3}(c^{1/3}+c^{2/3})-1 ?

The solution to expand c^{1/3}(c^{1/3}+c^{2/3})-1 is c^{2/3}+c-1

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expand c^{1/3}(c^{1/3}+c^{2/3})-1

expand

c^{\frac{1}{3}} (c^{\frac{1}{3}} + c^{\frac{2}{3}}) - 1

c^{\frac{2}{3}} + c - 1

Solution steps

c^{\frac{1}{3}} (c^{\frac{1}{3}} + c^{\frac{2}{3}}) - 1

Apply the distributive law:

a (b + c) = ab + a c

c^{\frac{1}{3}} (c^{\frac{1}{3}} + c^{\frac{2}{3}}) = c^{\frac{1}{3}} c^{\frac{1}{3}} + c^{\frac{1}{3}} c^{\frac{2}{3}}

= c^{\frac{1}{3}} c^{\frac{1}{3}} + c^{\frac{1}{3}} c^{\frac{2}{3}} - 1

c^{\frac{1}{3}} c^{\frac{1}{3}} = c^{\frac{2}{3}}

c^{\frac{1}{3}} c^{\frac{2}{3}} = c

= c^{\frac{2}{3}} + c - 1

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What is expand c^{1/3}(c^{1/3}+c^{2/3})-1 ?
The solution to expand c^{1/3}(c^{1/3}+c^{2/3})-1 is c^{2/3}+c-1