展开 (1+2x+3x^2)^6

解答

展开

(1 + 2 x + 3 x^{2})^{6}

729 x^{12} + 2916 x^{11} + 6318 x^{10} + 9180 x^{9} + 9855 x^{8} + 8136 x^{7} + 5284 x^{6} + 2712 x^{5} + 1095 x^{4} + 340 x^{3} + 78 x^{2} + 12 x + 1

求解步骤

(1 + 2 x + 3 x^{2})^{6}

(1 + 2 x + 3 x^{2})^{6} = (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2})

= (3 x^{2} + 2 x + 1) (3 x^{2} + 2 x + 1) (3 x^{2} + 2 x + 1) (3 x^{2} + 2 x + 1) (3 x^{2} + 2 x + 1) (3 x^{2} + 2 x + 1)

乘开

(1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) : 729 x^{12} + 2916 x^{11} + 6318 x^{10} + 9180 x^{9} + 9855 x^{8} + 8136 x^{7} + 5284 x^{6} + 2712 x^{5} + 1095 x^{4} + 340 x^{3} + 78 x^{2} + 12 x + 1

= 729 x^{12} + 2916 x^{11} + 6318 x^{10} + 9180 x^{9} + 9855 x^{8} + 8136 x^{7} + 5284 x^{6} + 2712 x^{5} + 1095 x^{4} + 340 x^{3} + 78 x^{2} + 12 x + 1

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

e x p an d - \frac{x ( - x + 3 ) ^{3}}{27}

e x p an d (y + y) 2 π

e x p an d \frac{4 ( b + 2 )}{3}

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