What is expand b^{1/3}(4b^{2/3}-b^{8/3}) ?

The solution to expand b^{1/3}(4b^{2/3}-b^{8/3}) is 4b-b^3

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expand b^{1/3}(4b^{2/3}-b^{8/3})

expand

b^{\frac{1}{3}} (4 b^{\frac{2}{3}} - b^{\frac{8}{3}})

4 b - b^{3}

Solution steps

b^{\frac{1}{3}} (4 b^{\frac{2}{3}} - b^{\frac{8}{3}})

Apply the distributive law:

a (b - c) = ab - a c

b^{\frac{1}{3}} (4 b^{\frac{2}{3}} - b^{\frac{8}{3}}) = b^{\frac{1}{3}} \cdot 4 b^{\frac{2}{3}} - b^{\frac{1}{3}} b^{\frac{8}{3}}

= b^{\frac{1}{3}} \cdot 4 b^{\frac{2}{3}} - b^{\frac{1}{3}} b^{\frac{8}{3}}

b^{\frac{1}{3}} \cdot 4 b^{\frac{2}{3}} = 4 b

b^{\frac{1}{3}} b^{\frac{8}{3}} = b^{3}

= 4 b - b^{3}

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What is expand b^{1/3}(4b^{2/3}-b^{8/3}) ?
The solution to expand b^{1/3}(4b^{2/3}-b^{8/3}) is 4b-b^3