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

الحلّ

expand

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

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

خطوات الحلّ

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

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

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

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

وسٌع:

n^{4} - 2 n^{3} + n^{2}

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

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

: استخدم ميزات الكسور التالية

\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}

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

اختزل:

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

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

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