What is expand x^{4/5}\times (x-4)^2 ?

The solution to expand x^{4/5}\times (x-4)^2 is x^{14/5}-8x^{9/5}+x^{4/5}*16

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expand x^{4/5}\times (x-4)^2

expand

x^{\frac{4}{5}} \cdot (x - 4)^{2}

x^{\frac{14}{5}} - 8 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 16

Solution steps

x^{\frac{4}{5}} (x - 4)^{2}

Expand

(x - 4)^{2} : x^{2} - 8 x + 16

= x^{\frac{4}{5}} (x^{2} - 8 x + 16)

Apply the distributive law:

m (a + b + c) = ma + mb + m c

x^{\frac{4}{5}} (x^{2} - 8 x + 16) = x^{\frac{4}{5}} x^{2} + x^{\frac{4}{5}} (- 8 x) + x^{\frac{4}{5}} \cdot 16

= x^{\frac{4}{5}} x^{2} + x^{\frac{4}{5}} (- 8 x) + x^{\frac{4}{5}} \cdot 16

x^{\frac{4}{5}} x^{2} = x^{\frac{14}{5}}

x^{\frac{4}{5}} (- 8 x) = - 8 x^{\frac{9}{5}}

= x^{\frac{14}{5}} - 8 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 16

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(- x^{2} + 8 \circ 4 x + 8) (- 4)

What is expand x^{4/5}\times (x-4)^2 ?
The solution to expand x^{4/5}\times (x-4)^2 is x^{14/5}-8x^{9/5}+x^{4/5}*16