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受欢迎的代数 >

展开 (((k+1)(k+1+1)(2(k+1)+1)))/6

解答

展开

\frac{( ( k + 1 ) ( k + 1 + 1 ) ( 2 ( k + 1 ) + 1 ) )}{6}

解答

\frac{k ^{3}}{3} + \frac{3 k ^{2}}{2} + \frac{13 k}{6} + 1

求解步骤

\frac{( k + 1 ) ( k + 1 + 1 ) ( 2 ( k + 1 ) + 1 )}{6}

数字相加:

1 + 1 = 2

= \frac{( k + 1 ) ( k + 2 ) ( 2 ( k + 1 ) + 1 )}{6}

乘开

2 (k + 1) + 1 : 2 k + 3

= \frac{( k + 1 ) ( k + 2 ) ( 2 k + 3 )}{6}

乘开

(k + 1) (k + 2) (2 k + 3) : 2 k^{3} + 9 k^{2} + 13 k + 6

= \frac{2 k ^{3} + 9 k ^{2} + 13 k + 6}{6}

使用分式法则:

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

\frac{2 k ^{3} + 9 k ^{2} + 13 k + 6}{6} = \frac{2 k ^{3}}{6} + \frac{9 k ^{2}}{6} + \frac{13 k}{6} + \frac{6}{6}

= \frac{2 k ^{3}}{6} + \frac{9 k ^{2}}{6} + \frac{13 k}{6} + \frac{6}{6}

使用法则

\frac{a}{a} = 1

\frac{6}{6} = 1

= \frac{2 k ^{3}}{6} + \frac{9 k ^{2}}{6} + \frac{13 k}{6} + 1

消掉

\frac{2 k ^{3}}{6} : \frac{k ^{3}}{3}

= \frac{k ^{3}}{3} + \frac{9 k ^{2}}{6} + \frac{13 k}{6} + 1

消掉

\frac{9 k ^{2}}{6} : \frac{3 k ^{2}}{2}

= \frac{k ^{3}}{3} + \frac{3 k ^{2}}{2} + \frac{13 k}{6} + 1

流行的例子

展开 (25)/((35s+1)(80s+1))

e x p an d \frac{25}{( 35 s + 1 ) ( 80 s + 1 )}

化简 (sqrt(3)x-2)^2

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

展开 (1+tan(x))(sec(x)tan(x))

e x p an d (1 + tan (x)) (sec (x) tan (x))

展开 ((k^2+k)/2)^2

e x p an d (\frac{k ^{2} + k}{2})^{2}

展开 (pi+i)^2

e x p an d (π + i)^{2}