확장 (x^3-x+30)^7

해법

확장

(x^{3} - x + 30)^{7}

x^{21} - 7 x^{19} + 210 x^{18} + 21 x^{17} - 1260 x^{16} + 18865 x^{15} + 3150 x^{14} - 94465 x^{13} + 940800 x^{12} + 188979 x^{11} - 3776850 x^{10} + 28161007 x^{9} + 5668740 x^{8} - 84955501 x^{7} + 506520210 x^{6} + 85031100 x^{5} - 1019655000 x^{4} + 5074650000 x^{3} + 510300000 x^{2} - 5103000000 x + 21870000000

솔루션 단계

(x^{3} - x + 30)^{7}

(x^{3} - x + 30)^{7} = (x^{3} - x + 30) (x^{3} - x + 30) (x^{3} - x + 30) (x^{3} - x + 30) (x^{3} - x + 30) (x^{3} - x + 30) (x^{3} - x + 30)

= (x^{3} - x + 30) (x^{3} - x + 30) (x^{3} - x + 30) (x^{3} - x + 30) (x^{3} - x + 30) (x^{3} - x + 30) (x^{3} - x + 30)

(x^{3} - x + 30) (x^{3} - x + 30) (x^{3} - x + 30) (x^{3} - x + 30) (x^{3} - x + 30) (x^{3} - x + 30) (x^{3} - x + 30)

확대한다:

x^{21} - 7 x^{19} + 210 x^{18} + 21 x^{17} - 1260 x^{16} + 18865 x^{15} + 3150 x^{14} - 94465 x^{13} + 940800 x^{12} + 188979 x^{11} - 3776850 x^{10} + 28161007 x^{9} + 5668740 x^{8} - 84955501 x^{7} + 506520210 x^{6} + 85031100 x^{5} - 1019655000 x^{4} + 5074650000 x^{3} + 510300000 x^{2} - 5103000000 x + 21870000000

= x^{21} - 7 x^{19} + 210 x^{18} + 21 x^{17} - 1260 x^{16} + 18865 x^{15} + 3150 x^{14} - 94465 x^{13} + 940800 x^{12} + 188979 x^{11} - 3776850 x^{10} + 28161007 x^{9} + 5668740 x^{8} - 84955501 x^{7} + 506520210 x^{6} + 85031100 x^{5} - 1019655000 x^{4} + 5074650000 x^{3} + 510300000 x^{2} - 5103000000 x + 21870000000