확장 ((4x^3-5x)^8)/8

해법

확장

\frac{( 4 x ^{3} - 5 x ) ^{8}}{8}

8192 x^{24} - 81920 x^{22} + 358400 x^{20} - 896000 x^{18} + 1400000 x^{16} - 1400000 x^{14} + 875000 x^{12} - 312500 x^{10} + \frac{390625 x ^{8}}{8}

솔루션 단계

\frac{( 4 x ^{3} - 5 x ) ^{8}}{8}

(4 x^{3} - 5 x)^{8} = 65536 x^{24} - 655360 x^{22} + 2867200 x^{20} - 7168000 x^{18} + 11200000 x^{16} - 11200000 x^{14} + 7000000 x^{12} - 2500000 x^{10} + 390625 x^{8}

= \frac{65536 x ^{24} - 655360 x ^{22} + 2867200 x ^{20} - 7168000 x ^{18} + 11200000 x ^{16} - 11200000 x ^{14} + 7000000 x ^{12} - 2500000 x ^{10} + 390625 x ^{8}}{8}

분수 규칙 적용:

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

\frac{65536 x ^{24} - 655360 x ^{22} + 2867200 x ^{20} - 7168000 x ^{18} + 11200000 x ^{16} - 11200000 x ^{14} + 7000000 x ^{12} - 2500000 x ^{10} + 390625 x ^{8}}{8} = \frac{65536 x ^{24}}{8} - \frac{655360 x ^{22}}{8} + \frac{2867200 x ^{20}}{8} - \frac{7168000 x ^{18}}{8} + \frac{11200000 x ^{16}}{8} - \frac{11200000 x ^{14}}{8} + \frac{7000000 x ^{12}}{8} - \frac{2500000 x ^{10}}{8} + \frac{390625 x ^{8}}{8}

= \frac{65536 x ^{24}}{8} - \frac{655360 x ^{22}}{8} + \frac{2867200 x ^{20}}{8} - \frac{7168000 x ^{18}}{8} + \frac{11200000 x ^{16}}{8} - \frac{11200000 x ^{14}}{8} + \frac{7000000 x ^{12}}{8} - \frac{2500000 x ^{10}}{8} + \frac{390625 x ^{8}}{8}

\frac{65536 x ^{24}}{8} = 8192 x^{24}

\frac{655360 x ^{22}}{8} = 81920 x^{22}

\frac{2867200 x ^{20}}{8} = 358400 x^{20}

\frac{7168000 x ^{18}}{8} = 896000 x^{18}

\frac{11200000 x ^{16}}{8} = 1400000 x^{16}

\frac{11200000 x ^{14}}{8} = 1400000 x^{14}

\frac{7000000 x ^{12}}{8} = 875000 x^{12}

\frac{2500000 x ^{10}}{8} = 312500 x^{10}

= 8192 x^{24} - 81920 x^{22} + 358400 x^{20} - 896000 x^{18} + 1400000 x^{16} - 1400000 x^{14} + 875000 x^{12} - 312500 x^{10} + \frac{390625 x ^{8}}{8}