展开 \sqrt[8]{n(n^2+1)(n^4+1)(n^8+1)+1}

解答

展开

8 n (n^{2} + 1) (n^{4} + 1) (n^{8} + 1) + 1

8 n^{15} + n^{7} + n^{11} + n^{3} + n^{13} + n^{5} + n^{9} + n + 1

求解步骤

8 n (n^{2} + 1) (n^{4} + 1) (n^{8} + 1) + 1

乘开

n (n^{2} + 1) (n^{4} + 1) (n^{8} + 1) + 1 : n^{15} + n^{7} + n^{11} + n^{3} + n^{13} + n^{5} + n^{9} + n + 1

= 8 n^{15} + n^{7} + n^{11} + n^{3} + n^{13} + n^{5} + n^{9} + n + 1

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

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

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

e x p an d (- 1, 5) y (2, - 1)

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