展开 ((n+1)(n+2)(n+3)(n+4))/4

解答

展开

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

\frac{n ^{4}}{4} + \frac{5 n ^{3}}{2} + \frac{35 n ^{2}}{4} + \frac{25 n}{2} + 6

求解步骤

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

乘开

(n + 1) (n + 2) (n + 3) (n + 4) : n^{4} + 10 n^{3} + 35 n^{2} + 50 n + 24

= \frac{n ^{4} + 10 n ^{3} + 35 n ^{2} + 50 n + 24}{4}

使用分式法则:

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

\frac{n ^{4} + 10 n ^{3} + 35 n ^{2} + 50 n + 24}{4} = \frac{n ^{4}}{4} + \frac{10 n ^{3}}{4} + \frac{35 n ^{2}}{4} + \frac{50 n}{4} + \frac{24}{4}

= \frac{n ^{4}}{4} + \frac{10 n ^{3}}{4} + \frac{35 n ^{2}}{4} + \frac{50 n}{4} + \frac{24}{4}

消掉

\frac{10 n ^{3}}{4} : \frac{5 n ^{3}}{2}

= \frac{n ^{4}}{4} + \frac{5 n ^{3}}{2} + \frac{35 n ^{2}}{4} + \frac{50 n}{4} + \frac{24}{4}

消掉

\frac{50 n}{4} : \frac{25 n}{2}

= \frac{n ^{4}}{4} + \frac{5 n ^{3}}{2} + \frac{35 n ^{2}}{4} + \frac{25 n}{2} + \frac{24}{4}

数字相除:

\frac{24}{4} = 6

= \frac{n ^{4}}{4} + \frac{5 n ^{3}}{2} + \frac{35 n ^{2}}{4} + \frac{25 n}{2} + 6

e x p an d \frac{125 ( 2 n + 1 ) ( n + 1 )}{6}

e x p an d \frac{( 3 )}{( ( x + 1 ) ( x + 2 ) )}

e x p an d lo g_{3} (x - 2)

e x p an d 16 ((x^{6 c} + 2 y^{5}) (x^{6 c} - 2 y^{5}))

s im pl i f y (3 x - 1)^{2}