展开 (3(n+1)(2n+1))/2

解答

展开

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

3 n^{2} + \frac{9 n}{2} + \frac{3}{2}

求解步骤

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

乘开

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

= \frac{6 n ^{2} + 9 n + 3}{2}

使用分式法则:

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

\frac{6 n ^{2} + 9 n + 3}{2} = \frac{6 n ^{2}}{2} + \frac{9 n}{2} + \frac{3}{2}

= \frac{6 n ^{2}}{2} + \frac{9 n}{2} + \frac{3}{2}

数字相除:

\frac{6}{2} = 3

= 3 n^{2} + \frac{9 n}{2} + \frac{3}{2}

e x p an d - \frac{2 ( y + 6 )}{3}

s im pl i f y (3 + 2 sin (θ)) (sin (θ))

e x p an d \frac{( c d + ab ) ( c - d )}{- b d + a c}

e x p an d \frac{2 ( 3 x - 1 ) ( - 3 x ^{2} + 2 x + 6 )}{( x ^{2} + 2 ) ^{3}}

s im pl i f y 25 (2185 - 35)