What is expand p^{2/3}(p^{1/3}+2p^{4/3}) ?

The solution to expand p^{2/3}(p^{1/3}+2p^{4/3}) is p+2p^2

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expand p^{2/3}(p^{1/3}+2p^{4/3})

expand

p^{\frac{2}{3}} (p^{\frac{1}{3}} + 2 p^{\frac{4}{3}})

p + 2 p^{2}

Solution steps

p^{\frac{2}{3}} (p^{\frac{1}{3}} + 2 p^{\frac{4}{3}})

Apply the distributive law:

a (b + c) = ab + a c

p^{\frac{2}{3}} (p^{\frac{1}{3}} + 2 p^{\frac{4}{3}}) = p^{\frac{2}{3}} p^{\frac{1}{3}} + p^{\frac{2}{3}} \cdot 2 p^{\frac{4}{3}}

= p^{\frac{2}{3}} p^{\frac{1}{3}} + p^{\frac{2}{3}} \cdot 2 p^{\frac{4}{3}}

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

p^{\frac{2}{3}} \cdot 2 p^{\frac{4}{3}} = 2 p^{2}

= p + 2 p^{2}

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cot (x) \cdot (cos (2 x) - 1)

What is expand p^{2/3}(p^{1/3}+2p^{4/3}) ?
The solution to expand p^{2/3}(p^{1/3}+2p^{4/3}) is p+2p^2