展开 (x^2+x-1)^{10}

解答

展开

(x^{2} + x - 1)^{10}

x^{20} + 10 x^{19} + 35 x^{18} + 30 x^{17} - 105 x^{16} - 228 x^{15} + 90 x^{14} + 540 x^{13} + 45 x^{12} - 770 x^{11} - 131 x^{10} + 770 x^{9} + 45 x^{8} - 540 x^{7} + 90 x^{6} + 228 x^{5} - 105 x^{4} - 30 x^{3} + 35 x^{2} - 10 x + 1

求解步骤

(x^{2} + x - 1)^{10}

(x^{2} + x - 1)^{10} = (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1)

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

乘开

(x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) : x^{20} + 10 x^{19} + 35 x^{18} + 30 x^{17} - 105 x^{16} - 228 x^{15} + 90 x^{14} + 540 x^{13} + 45 x^{12} - 770 x^{11} - 131 x^{10} + 770 x^{9} + 45 x^{8} - 540 x^{7} + 90 x^{6} + 228 x^{5} - 105 x^{4} - 30 x^{3} + 35 x^{2} - 10 x + 1

= x^{20} + 10 x^{19} + 35 x^{18} + 30 x^{17} - 105 x^{16} - 228 x^{15} + 90 x^{14} + 540 x^{13} + 45 x^{12} - 770 x^{11} - 131 x^{10} + 770 x^{9} + 45 x^{8} - 540 x^{7} + 90 x^{6} + 228 x^{5} - 105 x^{4} - 30 x^{3} + 35 x^{2} - 10 x + 1

e x p an d \frac{( x - 1 ) y}{x}

e x p an d e^{2} + b^{2} + c^{2} + 2 (ab + b c + a c)

e x p an d t^{'} F (t) (3 t - 7)^{2}

e x p an d \frac{32 x ^{2}}{( x - 6 ) ( x + 2 ) ^{2}}

e x p an d \frac{x}{( s ^{2} + x ^{2} ) ( s ^{2} + 4 s + 13 )}