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受欢迎的代数 >

展开 (z^2(1+2z)^3)/6

解答

展开

\frac{z ^{2} ( 1 + 2 z ) ^{3}}{6}

解答

\frac{4 z ^{5}}{3} + 2 z^{4} + z^{3} + \frac{z ^{2}}{6}

求解步骤

\frac{z ^{2} ( 1 + 2 z ) ^{3}}{6}

(1 + 2 z)^{3} = 1 + 6 z + 12 z^{2} + 8 z^{3}

= \frac{z ^{2} ( 8 z ^{3} + 12 z ^{2} + 6 z + 1 )}{6}

乘开

z^{2} (1 + 6 z + 12 z^{2} + 8 z^{3}) : z^{2} + 6 z^{3} + 12 z^{4} + 8 z^{5}

= \frac{z ^{2} + 6 z ^{3} + 12 z ^{4} + 8 z ^{5}}{6}

使用分式法则:

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

\frac{z ^{2} + 6 z ^{3} + 12 z ^{4} + 8 z ^{5}}{6} = \frac{z ^{2}}{6} + \frac{6 z ^{3}}{6} + \frac{12 z ^{4}}{6} + \frac{8 z ^{5}}{6}

= \frac{z ^{2}}{6} + \frac{6 z ^{3}}{6} + \frac{12 z ^{4}}{6} + \frac{8 z ^{5}}{6}

数字相除:

\frac{6}{6} = 1

= \frac{z ^{2}}{6} + z^{3} + \frac{12 z ^{4}}{6} + \frac{8 z ^{5}}{6}

数字相除:

\frac{12}{6} = 2

= \frac{z ^{2}}{6} + z^{3} + 2 z^{4} + \frac{8 z ^{5}}{6}

消掉

\frac{8 z ^{5}}{6} : \frac{4 z ^{5}}{3}

= \frac{z ^{2}}{6} + z^{3} + 2 z^{4} + \frac{4 z ^{5}}{3}

改写为标准形式

= \frac{4 z ^{5}}{3} + 2 z^{4} + z^{3} + \frac{z ^{2}}{6}

流行的例子

展开 cos(3(90-c))

e x p an d cos (3 (9 0^{\circ} - c))

展开 (-59)+(-1)

e x p an d (- 59) + (- 1)

展开 20(e^{-x}-e^{-x}x)

e x p an d 20 (e^{- x} - e^{- x} x)

e x p an d Q (6, - 7)

展开 1/((kv+g)(g-2kv))

e x p an d \frac{1}{( k v + g ) ( g - 2 k v )}