展开 (x^2+4x-2)^9

解答

展开

(x^{2} + 4 x - 2)^{9}

x^{18} + 36 x^{17} + 558 x^{16} + 4800 x^{15} + 24336 x^{14} + 68544 x^{13} + 69216 x^{12} - 135936 x^{11} - 343584 x^{10} + 179584 x^{9} + 687168 x^{8} - 543744 x^{7} - 553728 x^{6} + 1096704 x^{5} - 778752 x^{4} + 307200 x^{3} - 71424 x^{2} + 9216 x - 512

求解步骤

(x^{2} + 4 x - 2)^{9}

(x^{2} + 4 x - 2)^{9} = (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2)

= (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2)

乘开

(x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) (x^{2} + 4 x - 2) : x^{18} + 36 x^{17} + 558 x^{16} + 4800 x^{15} + 24336 x^{14} + 68544 x^{13} + 69216 x^{12} - 135936 x^{11} - 343584 x^{10} + 179584 x^{9} + 687168 x^{8} - 543744 x^{7} - 553728 x^{6} + 1096704 x^{5} - 778752 x^{4} + 307200 x^{3} - 71424 x^{2} + 9216 x - 512

= x^{18} + 36 x^{17} + 558 x^{16} + 4800 x^{15} + 24336 x^{14} + 68544 x^{13} + 69216 x^{12} - 135936 x^{11} - 343584 x^{10} + 179584 x^{9} + 687168 x^{8} - 543744 x^{7} - 553728 x^{6} + 1096704 x^{5} - 778752 x^{4} + 307200 x^{3} - 71424 x^{2} + 9216 x - 512

e x p an d \frac{( 2 x + 5 ) ^{4}}{8}

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e x p an d A (- 1, 4) B (6, - 3)

e x p an d \frac{( 2 x ^{3} - 1 ) ^{6}}{64 x ^{6}}

e x p an d y (2 x e^{x y} + e^{x y} y x^{2})