展开 ((16-9r^2)^3)/3

解答

展开

\frac{( 16 - 9 r ^{2} ) ^{3}}{3}

- 243 r^{6} + 1296 r^{4} - 2304 r^{2} + \frac{4096}{3}

求解步骤

\frac{( 16 - 9 r ^{2} ) ^{3}}{3}

(16 - 9 r^{2})^{3} = 4096 - 6912 r^{2} + 3888 r^{4} - 729 r^{6}

= \frac{4096 - 6912 r ^{2} + 3888 r ^{4} - 729 r ^{6}}{3}

使用分式法则:

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

\frac{4096 - 6912 r ^{2} + 3888 r ^{4} - 729 r ^{6}}{3} = \frac{4096}{3} - \frac{6912 r ^{2}}{3} + \frac{3888 r ^{4}}{3} - \frac{729 r ^{6}}{3}

= \frac{4096}{3} - \frac{6912 r ^{2}}{3} + \frac{3888 r ^{4}}{3} - \frac{729 r ^{6}}{3}

数字相除:

\frac{6912}{3} = 2304

= \frac{4096}{3} - 2304 r^{2} + \frac{3888 r ^{4}}{3} - \frac{729 r ^{6}}{3}

数字相除:

\frac{3888}{3} = 1296

= \frac{4096}{3} - 2304 r^{2} + 1296 r^{4} - \frac{729 r ^{6}}{3}

数字相除:

\frac{729}{3} = 243

= \frac{4096}{3} - 2304 r^{2} + 1296 r^{4} - 243 r^{6}

改写为标准形式

= - 243 r^{6} + 1296 r^{4} - 2304 r^{2} + \frac{4096}{3}

s im pl i f y 3 \cdot δ (x - 2) + 11 \cdot H (x - 10)

e x p an d (x^{2} - 2 x - 3) \cdot ln^{2} (x - 1)

\frac{d}{d t} ((s (t)) (4 t^{2} - 6 t - 5))

e x p an d (3 y + 15)^{\circ} (3 y + 15) + (2 y + 5)

e x p an d \frac{12 x ^{2} + 18}{x ( x ^{2} + 4 )}