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}

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