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

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

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

expand

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

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

Solution steps

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

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

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

Expand

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{2}{2} = 1

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

(a + b)^{(a + b) 2}

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\frac{d}{d t} ((x) (x t + x) e^{t})

(e^{x} - e^{- 5 x})^{2}

\frac{1}{x ( x + b )}

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