What is expand (20(-1+k/n)^3+20(-1+k/n)^2)*1/n ?

The solution to expand (20(-1+k/n)^3+20(-1+k/n)^2)*1/n is (20(-n+k)^3)/(n^4)+(20(-n+k)^2)/(n^3)

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expand (20(-1+k/n)^3+20(-1+k/n)^2)*1/n

expand

(20 (- 1 + \frac{k}{n})^{3} + 20 (- 1 + \frac{k}{n})^{2}) \cdot \frac{1}{n}

\frac{20 ( - n + k ) ^{3}}{n ^{4}} + \frac{20 ( - n + k ) ^{2}}{n ^{3}}

Solution steps

(20 (- 1 + \frac{k}{n})^{3} + 20 (- 1 + \frac{k}{n})^{2}) \frac{1}{n}

= \frac{1}{n} (20 (- 1 + \frac{k}{n})^{3} + 20 (- 1 + \frac{k}{n})^{2})

Apply the distributive law:

a (b + c) = ab + a c

\frac{1}{n} (20 (- 1 + \frac{k}{n})^{3} + 20 (- 1 + \frac{k}{n})^{2}) = \frac{1}{n} \cdot 20 (- 1 + \frac{k}{n})^{3} + \frac{1}{n} \cdot 20 (- 1 + \frac{k}{n})^{2}

= \frac{1}{n} \cdot 20 (- 1 + \frac{k}{n})^{3} + \frac{1}{n} \cdot 20 (- 1 + \frac{k}{n})^{2}

Simplify

\frac{1}{n} \cdot 20 (- 1 + \frac{k}{n})^{3} + \frac{1}{n} \cdot 20 (- 1 + \frac{k}{n})^{2} : \frac{20 ( - n + k ) ^{3}}{n ^{4}} + \frac{20 ( - n + k ) ^{2}}{n ^{3}}

= \frac{20 ( - n + k ) ^{3}}{n ^{4}} + \frac{20 ( - n + k ) ^{2}}{n ^{3}}

- \frac{1}{4} (x - 34)^{2} (x - 41) + 45

\frac{1}{( s + 3 ) ( s ^{2} - 5 s + 10 )}

\frac{d y}{y} (- 3, - 5) (0, 10)^{''}

\frac{1}{5} (3 ln \frac{x ^{2}}{4} + 1 + 2 arctan (\frac{x}{2}))

\frac{3 x ^{3} + 2 x - 1}{x ( x + 1 ) ( x - 7 )}

What is expand (20(-1+k/n)^3+20(-1+k/n)^2)*1/n ?
The solution to expand (20(-1+k/n)^3+20(-1+k/n)^2)*1/n is (20(-n+k)^3)/(n^4)+(20(-n+k)^2)/(n^3)