展开 (n^2(n+1)^2)/2

解答

展开

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

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

求解步骤

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

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

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

乘开

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

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

使用分式法则:

\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}

数字相除:

\frac{2}{2} = 1

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

e x p an d (a + b)^{(a + b) 2}

e x p an d \frac{20 ( 14 + 5 3 )}{3}

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

e x p an d (e^{x} - e^{- 5 x})^{2}

e x p an d \frac{1}{x ( x + b )}