展开 (a(a^2-4)^3)/8

解答

展开

\frac{a ( a ^{2} - 4 ) ^{3}}{8}

\frac{a ^{7}}{8} - \frac{3 a ^{5}}{2} + 6 a^{3} - 8 a

求解步骤

\frac{a ( a ^{2} - 4 ) ^{3}}{8}

(a^{2} - 4)^{3} = a^{6} - 12 a^{4} + 48 a^{2} - 64

= \frac{a ( a ^{6} - 12 a ^{4} + 48 a ^{2} - 64 )}{8}

乘开

a (a^{6} - 12 a^{4} + 48 a^{2} - 64) : a^{7} - 12 a^{5} + 48 a^{3} - 64 a

= \frac{a ^{7} - 12 a ^{5} + 48 a ^{3} - 64 a}{8}

使用分式法则:

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

\frac{a ^{7} - 12 a ^{5} + 48 a ^{3} - 64 a}{8} = \frac{a ^{7}}{8} - \frac{12 a ^{5}}{8} + \frac{48 a ^{3}}{8} - \frac{64 a}{8}

= \frac{a ^{7}}{8} - \frac{12 a ^{5}}{8} + \frac{48 a ^{3}}{8} - \frac{64 a}{8}

消掉

\frac{12 a ^{5}}{8} : \frac{3 a ^{5}}{2}

= \frac{a ^{7}}{8} - \frac{3 a ^{5}}{2} + \frac{48 a ^{3}}{8} - \frac{64 a}{8}

数字相除:

\frac{48}{8} = 6

= \frac{a ^{7}}{8} - \frac{3 a ^{5}}{2} + 6 a^{3} - \frac{64 a}{8}

数字相除:

\frac{64}{8} = 8

= \frac{a ^{7}}{8} - \frac{3 a ^{5}}{2} + 6 a^{3} - 8 a

e x p an d (4 sin (3 x) csc (2 x) - 3 tan (x)) csc (x) - 4

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

\frac{d}{d x} ((z) (x^{2} + y^{2} + z^{2}))

e x p an d \frac{5 ( 4 - 3 x ^{2} )}{( 4 + 3 x ^{2} ) ^{2}}

e x p an d (3 e + 4 f)^{8}