What is (n^2(n+1)^2)/4+(n+1)^3 ?

The solution to (n^2(n+1)^2)/4+(n+1)^3 is (n^4+6n^3+13n^2+12n+4)/4

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simplify (n^2(n+1)^2)/4+(n+1)^3

simplify

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

\frac{n ^{4} + 6 n ^{3} + 13 n ^{2} + 12 n + 4}{4}

Solution steps

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

Apply the fraction rule:

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

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

Simplify

(n + 1)^{3} \cdot 4 + n^{2} (n + 1)^{2} : n^{4} + 6 n^{3} + 13 n^{2} + 12 n + 4

= \frac{n ^{4} + 6 n ^{3} + 13 n ^{2} + 12 n + 4}{4}

4 ln (e)

- \frac{1}{5} + \frac{3}{5}

(x - 2) (x - 3)^{2}

e^{l n (1 + x)}

4 \frac{2}{15} \div 3.1

What is (n^2(n+1)^2)/4+(n+1)^3 ?
The solution to (n^2(n+1)^2)/4+(n+1)^3 is (n^4+6n^3+13n^2+12n+4)/4