展开 18((x-1)^3(x-3)^{11})

解答

展开

18 ((x - 1)^{3} (x - 3)^{11})

18 x^{14} - 648 x^{13} + 10746 x^{12} - 108720 x^{11} + 749034 x^{10} - 3713688 x^{9} + 13648338 x^{8} - 37721376 x^{7} + 78666390 x^{6} - 122979384 x^{5} + 141599502 x^{4} - 116208432 x^{3} + 64127214 x^{2} - 21257640 x + 3188646

求解步骤

18 ((x - 1)^{3} (x - 3)^{11})

去除括号:

(a) = a

= 18 (x - 1)^{3} (x - 3)^{11}

(x - 1)^{3} = x^{3} - 3 x^{2} + 3 x - 1

= 18 (x^{3} - 3 x^{2} + 3 x - 1) (x - 3)^{11}

(x - 3)^{11} = x^{11} - 33 x^{10} + 495 x^{9} - 4455 x^{8} + 26730 x^{7} - 112266 x^{6} + 336798 x^{5} - 721710 x^{4} + 1082565 x^{3} - 1082565 x^{2} + 649539 x - 177147

= 18 (x^{3} - 3 x^{2} + 3 x - 1) (x^{11} - 33 x^{10} + 495 x^{9} - 4455 x^{8} + 26730 x^{7} - 112266 x^{6} + 336798 x^{5} - 721710 x^{4} + 1082565 x^{3} - 1082565 x^{2} + 649539 x - 177147)

乘开

(x^{3} - 3 x^{2} + 3 x - 1) (x^{11} - 33 x^{10} + 495 x^{9} - 4455 x^{8} + 26730 x^{7} - 112266 x^{6} + 336798 x^{5} - 721710 x^{4} + 1082565 x^{3} - 1082565 x^{2} + 649539 x - 177147) : x^{14} - 36 x^{13} + 597 x^{12} - 6040 x^{11} + 41613 x^{10} - 206316 x^{9} + 758241 x^{8} - 2095632 x^{7} + 4370355 x^{6} - 6832188 x^{5} + 7866639 x^{4} - 6456024 x^{3} + 3562623 x^{2} - 1180980 x + 177147

= 18 (x^{14} - 36 x^{13} + 597 x^{12} - 6040 x^{11} + 41613 x^{10} - 206316 x^{9} + 758241 x^{8} - 2095632 x^{7} + 4370355 x^{6} - 6832188 x^{5} + 7866639 x^{4} - 6456024 x^{3} + 3562623 x^{2} - 1180980 x + 177147)

乘开

18 (x^{14} - 36 x^{13} + 597 x^{12} - 6040 x^{11} + 41613 x^{10} - 206316 x^{9} + 758241 x^{8} - 2095632 x^{7} + 4370355 x^{6} - 6832188 x^{5} + 7866639 x^{4} - 6456024 x^{3} + 3562623 x^{2} - 1180980 x + 177147) : 18 x^{14} - 648 x^{13} + 10746 x^{12} - 108720 x^{11} + 749034 x^{10} - 3713688 x^{9} + 13648338 x^{8} - 37721376 x^{7} + 78666390 x^{6} - 122979384 x^{5} + 141599502 x^{4} - 116208432 x^{3} + 64127214 x^{2} - 21257640 x + 3188646

= 18 x^{14} - 648 x^{13} + 10746 x^{12} - 108720 x^{11} + 749034 x^{10} - 3713688 x^{9} + 13648338 x^{8} - 37721376 x^{7} + 78666390 x^{6} - 122979384 x^{5} + 141599502 x^{4} - 116208432 x^{3} + 64127214 x^{2} - 21257640 x + 3188646

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