What is expand (n^2(n+1)^2)/4+(n+1) ?

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

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expand (n^2(n+1)^2)/4+(n+1)

expand

\frac{n ^{2} ( n + 1 ) ^{2}}{4} + (n + 1)

\frac{n ^{4}}{4} + \frac{n ^{3}}{2} + \frac{n ^{2}}{4} + n + 1

Solution steps

\frac{n ^{2} ( n + 1 ) ^{2}}{4} + (n + 1)

Remove parentheses:

(a) = a

= \frac{n ^{2} ( n + 1 ) ^{2}}{4} + n + 1

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

= \frac{n ^{4} + 2 n ^{3} + n ^{2}}{4} + n + 1

Apply the fraction rule:

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

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

= \frac{n ^{4}}{4} + \frac{2 n ^{3}}{4} + \frac{n ^{2}}{4} + n + 1

Cancel

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

= \frac{n ^{4}}{4} + \frac{n ^{3}}{2} + \frac{n ^{2}}{4} + n + 1

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