What is expand (n^2(n+1)^2)/3 ?

The solution to expand (n^2(n+1)^2)/3 is (n^4)/3+(2n^3)/3+(n^2)/3

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expand (n^2(n+1)^2)/3

expand

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

\frac{n ^{4}}{3} + \frac{2 n ^{3}}{3} + \frac{n ^{2}}{3}

Solution steps

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

(n + 1)^{2} = n^{2} + 2 n + 1

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

Expand

n^{2} (n^{2} + 2 n + 1) : n^{4} + 2 n^{3} + n^{2}

= \frac{n ^{4} + 2 n ^{3} + n ^{2}}{3}

Apply the fraction rule:

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

\frac{n ^{4} + 2 n ^{3} + n ^{2}}{3} = \frac{n ^{4}}{3} + \frac{2 n ^{3}}{3} + \frac{n ^{2}}{3}

= \frac{n ^{4}}{3} + \frac{2 n ^{3}}{3} + \frac{n ^{2}}{3}

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

(0 - 2 - 2) x (231) x (- 2, 1, 2)

e^{(x^{2} - 3) (x + 4)}

(2 π + 16) \cdot 10

\frac{3 x ( x ^{2} - 5 )}{x ^{2} - 1}

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