展开 (x^2+2x+1)^6

解答

展开

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

x^{12} + 12 x^{11} + 66 x^{10} + 220 x^{9} + 495 x^{8} + 792 x^{7} + 924 x^{6} + 792 x^{5} + 495 x^{4} + 220 x^{3} + 66 x^{2} + 12 x + 1

求解步骤

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

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

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

乘开

(x^{2} + 2 x + 1) (x^{2} + 2 x + 1) (x^{2} + 2 x + 1) (x^{2} + 2 x + 1) (x^{2} + 2 x + 1) (x^{2} + 2 x + 1) : x^{12} + 12 x^{11} + 66 x^{10} + 220 x^{9} + 495 x^{8} + 792 x^{7} + 924 x^{6} + 792 x^{5} + 495 x^{4} + 220 x^{3} + 66 x^{2} + 12 x + 1

= x^{12} + 12 x^{11} + 66 x^{10} + 220 x^{9} + 495 x^{8} + 792 x^{7} + 924 x^{6} + 792 x^{5} + 495 x^{4} + 220 x^{3} + 66 x^{2} + 12 x + 1

e x p an d \frac{( x ^{4} - 2 x ^{3} + 5 x ^{2} - 3 x + 4 )}{( x - 1 ) ( x + 2 )}

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

e x p an d - \frac{x ^{2} + 6 x + 21}{( x ^{2} - 3 ) ( x + 4 )}

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

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