What is expand (n^2(n+3)^3)/2 ?

The solution to expand (n^2(n+3)^3)/2 is (n^5)/2+(9n^4)/2+(27n^3)/2+(27n^2)/2

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expand (n^2(n+3)^3)/2

expand

\frac{n ^{2} ( n + 3 ) ^{3}}{2}

\frac{n ^{5}}{2} + \frac{9 n ^{4}}{2} + \frac{27 n ^{3}}{2} + \frac{27 n ^{2}}{2}

Solution steps

\frac{n ^{2} ( n + 3 ) ^{3}}{2}

(n + 3)^{3} = n^{3} + 9 n^{2} + 27 n + 27

= \frac{n ^{2} ( n ^{3} + 9 n ^{2} + 27 n + 27 )}{2}

Expand

n^{2} (n^{3} + 9 n^{2} + 27 n + 27) : n^{5} + 9 n^{4} + 27 n^{3} + 27 n^{2}

= \frac{n ^{5} + 9 n ^{4} + 27 n ^{3} + 27 n ^{2}}{2}

Apply the fraction rule:

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

\frac{n ^{5} + 9 n ^{4} + 27 n ^{3} + 27 n ^{2}}{2} = \frac{n ^{5}}{2} + \frac{9 n ^{4}}{2} + \frac{27 n ^{3}}{2} + \frac{27 n ^{2}}{2}

= \frac{n ^{5}}{2} + \frac{9 n ^{4}}{2} + \frac{27 n ^{3}}{2} + \frac{27 n ^{2}}{2}

\frac{( cos ( x ) + 1 )}{( x - π ) ^{2}}

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

(y^{2} + \frac{5}{2}) (y^{2} - \frac{3}{2})

(- \frac{x ^{3}}{4} + 2 y) \cdot (3 x^{2} - x y + y^{4})

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

What is expand (n^2(n+3)^3)/2 ?
The solution to expand (n^2(n+3)^3)/2 is (n^5)/2+(9n^4)/2+(27n^3)/2+(27n^2)/2