What is expand (n(n+1)(6n^3+9n^2+n-1))/(30) ?

The solution to expand (n(n+1)(6n^3+9n^2+n-1))/(30) is (n^5)/5+(n^4)/2+(n^3)/3-n/(30)

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expand (n(n+1)(6n^3+9n^2+n-1))/(30)

expand

\frac{n ( n + 1 ) ( 6 n ^{3} + 9 n ^{2} + n - 1 )}{30}

\frac{n ^{5}}{5} + \frac{n ^{4}}{2} + \frac{n ^{3}}{3} - \frac{n}{30}

Solution steps

\frac{n ( n + 1 ) ( 6 n ^{3} + 9 n ^{2} + n - 1 )}{30}

Expand

n (n + 1) (6 n^{3} + 9 n^{2} + n - 1) : 6 n^{5} + 15 n^{4} + 10 n^{3} - n

= \frac{6 n ^{5} + 15 n ^{4} + 10 n ^{3} - n}{30}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{6 n ^{5} + 15 n ^{4} + 10 n ^{3} - n}{30} = \frac{6 n ^{5}}{30} + \frac{15 n ^{4}}{30} + \frac{10 n ^{3}}{30} - \frac{n}{30}

= \frac{6 n ^{5}}{30} + \frac{15 n ^{4}}{30} + \frac{10 n ^{3}}{30} - \frac{n}{30}

Cancel

\frac{6 n ^{5}}{30} : \frac{n ^{5}}{5}

= \frac{n ^{5}}{5} + \frac{15 n ^{4}}{30} + \frac{10 n ^{3}}{30} - \frac{n}{30}

Cancel

\frac{15 n ^{4}}{30} : \frac{n ^{4}}{2}

= \frac{n ^{5}}{5} + \frac{n ^{4}}{2} + \frac{10 n ^{3}}{30} - \frac{n}{30}

Cancel

\frac{10 n ^{3}}{30} : \frac{n ^{3}}{3}

= \frac{n ^{5}}{5} + \frac{n ^{4}}{2} + \frac{n ^{3}}{3} - \frac{n}{30}

2 x^{2} \cdot ((1 + x^{2}) y^{'} (x) + 4 x y)

\frac{( x + 8 ) ^{2}}{2}

\frac{9 - x}{x ( 2 x - 5 ) ( x - 4 )}

(x + y 2 - x^{2}) d y

(1 - x) ln^{x} (x)

What is expand (n(n+1)(6n^3+9n^2+n-1))/(30) ?
The solution to expand (n(n+1)(6n^3+9n^2+n-1))/(30) is (n^5)/5+(n^4)/2+(n^3)/3-n/(30)