展开-(z^2(-2z+6)^2)/9

解答

展开

- \frac{z ^{2} ( - 2 z + 6 ) ^{2}}{9}

- \frac{4 z ^{4}}{9} + \frac{8 z ^{3}}{3} - 4 z^{2}

求解步骤

- \frac{z ^{2} ( - 2 z + 6 ) ^{2}}{9}

(- 2 z + 6)^{2} = 4 z^{2} - 24 z + 36

= - \frac{z ^{2} ( 4 z ^{2} - 24 z + 36 )}{9}

乘开

z^{2} (4 z^{2} - 24 z + 36) : 4 z^{4} - 24 z^{3} + 36 z^{2}

= - \frac{4 z ^{4} - 24 z ^{3} + 36 z ^{2}}{9}

使用分式法则:

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

\frac{4 z ^{4} - 24 z ^{3} + 36 z ^{2}}{9} = - (\frac{4 z ^{4}}{9}) - (- \frac{24 z ^{3}}{9}) - (\frac{36 z ^{2}}{9})

= - (\frac{4 z ^{4}}{9}) - (- \frac{24 z ^{3}}{9}) - (\frac{36 z ^{2}}{9})

去除括号:

(a) = a, - (- a) = a

= - \frac{4 z ^{4}}{9} + \frac{24 z ^{3}}{9} - \frac{36 z ^{2}}{9}

消掉

\frac{24 z ^{3}}{9} : \frac{8 z ^{3}}{3}

= - \frac{4 z ^{4}}{9} + \frac{8 z ^{3}}{3} - \frac{36 z ^{2}}{9}

数字相除:

\frac{36}{9} = 4

= - \frac{4 z ^{4}}{9} + \frac{8 z ^{3}}{3} - 4 z^{2}

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