What is expand x^{4/5}(10x-40)^2 ?

The solution to expand x^{4/5}(10x-40)^2 is 100x^{14/5}-800x^{9/5}+x^{4/5}*1600

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expand x^{4/5}(10x-40)^2

expand

x^{\frac{4}{5}} (10 x - 40)^{2}

100 x^{\frac{14}{5}} - 800 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 1600

Solution steps

x^{\frac{4}{5}} (10 x - 40)^{2}

Expand

(10 x - 40)^{2} : 100 x^{2} - 800 x + 1600

= x^{\frac{4}{5}} (100 x^{2} - 800 x + 1600)

Apply the distributive law:

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

x^{\frac{4}{5}} (100 x^{2} - 800 x + 1600) = x^{\frac{4}{5}} \cdot 100 x^{2} + x^{\frac{4}{5}} (- 800 x) + x^{\frac{4}{5}} \cdot 1600

= x^{\frac{4}{5}} \cdot 100 x^{2} + x^{\frac{4}{5}} (- 800 x) + x^{\frac{4}{5}} \cdot 1600

x^{\frac{4}{5}} \cdot 100 x^{2} = 100 x^{\frac{14}{5}}

x^{\frac{4}{5}} (- 800 x) = - 800 x^{\frac{9}{5}}

= 100 x^{\frac{14}{5}} - 800 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 1600

(2 a - 3 b)^{2}

\frac{1}{3} (x - 5)^{3}

(3 + 7) (2 + 10)

\frac{e ^{- x}}{x ( x - 3 ) ( x - 2 )}

2 y (3 x y - 4 y)

What is expand x^{4/5}(10x-40)^2 ?
The solution to expand x^{4/5}(10x-40)^2 is 100x^{14/5}-800x^{9/5}+x^{4/5}*1600