因式分解 3j^{112}+3j^{39}

解答

因式分解

3 j^{112} + 3 j^{39}

3 j^{39} (j + 1) (j^{72} - j^{71} + j^{70} - j^{69} + j^{68} - j^{67} + j^{66} - j^{65} + j^{64} - j^{63} + j^{62} - j^{61} + j^{60} - j^{59} + j^{58} - j^{57} + j^{56} - j^{55} + j^{54} - j^{53} + j^{52} - j^{51} + j^{50} - j^{49} + j^{48} - j^{47} + j^{46} - j^{45} + j^{44} - j^{43} + j^{42} - j^{41} + j^{40} - j^{39} + j^{38} - j^{37} + j^{36} - j^{35} + j^{34} - j^{33} + j^{32} - j^{31} + j^{30} - j^{29} + j^{28} - j^{27} + j^{26} - j^{25} + j^{24} - j^{23} + j^{22} - j^{21} + j^{20} - j^{19} + j^{18} - j^{17} + j^{16} - j^{15} + j^{14} - j^{13} + j^{12} - j^{11} + j^{10} - j^{9} + j^{8} - j^{7} + j^{6} - j^{5} + j^{4} - j^{3} + j^{2} - j + 1)

求解步骤

3 j^{112} + 3 j^{39}

因式分解出通项

3 j^{39} : 3 j^{39} (j^{73} + 1)

= 3 j^{39} (j^{73} + 1)

因式分解

j^{73} + 1 : (j + 1) (j^{72} - j^{71} + j^{70} - j^{69} + j^{68} - j^{67} + j^{66} - j^{65} + j^{64} - j^{63} + j^{62} - j^{61} + j^{60} - j^{59} + j^{58} - j^{57} + j^{56} - j^{55} + j^{54} - j^{53} + j^{52} - j^{51} + j^{50} - j^{49} + j^{48} - j^{47} + j^{46} - j^{45} + j^{44} - j^{43} + j^{42} - j^{41} + j^{40} - j^{39} + j^{38} - j^{37} + j^{36} - j^{35} + j^{34} - j^{33} + j^{32} - j^{31} + j^{30} - j^{29} + j^{28} - j^{27} + j^{26} - j^{25} + j^{24} - j^{23} + j^{22} - j^{21} + j^{20} - j^{19} + j^{18} - j^{17} + j^{16} - j^{15} + j^{14} - j^{13} + j^{12} - j^{11} + j^{10} - j^{9} + j^{8} - j^{7} + j^{6} - j^{5} + j^{4} - j^{3} + j^{2} - j + 1)

= 3 j^{39} (j + 1) (j^{72} - j^{71} + j^{70} - j^{69} + j^{68} - j^{67} + j^{66} - j^{65} + j^{64} - j^{63} + j^{62} - j^{61} + j^{60} - j^{59} + j^{58} - j^{57} + j^{56} - j^{55} + j^{54} - j^{53} + j^{52} - j^{51} + j^{50} - j^{49} + j^{48} - j^{47} + j^{46} - j^{45} + j^{44} - j^{43} + j^{42} - j^{41} + j^{40} - j^{39} + j^{38} - j^{37} + j^{36} - j^{35} + j^{34} - j^{33} + j^{32} - j^{31} + j^{30} - j^{29} + j^{28} - j^{27} + j^{26} - j^{25} + j^{24} - j^{23} + j^{22} - j^{21} + j^{20} - j^{19} + j^{18} - j^{17} + j^{16} - j^{15} + j^{14} - j^{13} + j^{12} - j^{11} + j^{10} - j^{9} + j^{8} - j^{7} + j^{6} - j^{5} + j^{4} - j^{3} + j^{2} - j + 1)

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