展开 (1+x+2x^2)^6

解答

展开

(1 + x + 2 x^{2})^{6}

64 x^{12} + 192 x^{11} + 432 x^{10} + 640 x^{9} + 780 x^{8} + 732 x^{7} + 581 x^{6} + 366 x^{5} + 195 x^{4} + 80 x^{3} + 27 x^{2} + 6 x + 1

求解步骤

(1 + x + 2 x^{2})^{6}

(1 + x + 2 x^{2})^{6} = (1 + x + 2 x^{2}) (1 + x + 2 x^{2}) (1 + x + 2 x^{2}) (1 + x + 2 x^{2}) (1 + x + 2 x^{2}) (1 + x + 2 x^{2})

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

乘开

(1 + x + 2 x^{2}) (1 + x + 2 x^{2}) (1 + x + 2 x^{2}) (1 + x + 2 x^{2}) (1 + x + 2 x^{2}) (1 + x + 2 x^{2}) : 64 x^{12} + 192 x^{11} + 432 x^{10} + 640 x^{9} + 780 x^{8} + 732 x^{7} + 581 x^{6} + 366 x^{5} + 195 x^{4} + 80 x^{3} + 27 x^{2} + 6 x + 1

= 64 x^{12} + 192 x^{11} + 432 x^{10} + 640 x^{9} + 780 x^{8} + 732 x^{7} + 581 x^{6} + 366 x^{5} + 195 x^{4} + 80 x^{3} + 27 x^{2} + 6 x + 1

s im pl i f y 3 (- \frac{y ^{3}}{3} - y + 4) (\frac{( - y ^{3} - 3 y + 12 ) ^{2}}{9} - 2)

e x p an d - x (2 x + y = 7)

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

s im pl i f y (3 z - 4 i)^{2}

e x p an d \frac{2 x ^{3} - 4 x ^{2} - 15 x + 8}{( x - 1 ) ^{2}}