展开 (160x^6+50000x^3)/(3(2x+5)^5)

解答

展开

\frac{160 x ^{6} + 50000 x ^{3}}{3 ( 2 x + 5 ) ^{5}}

\frac{160 x ^{6} + 50000 x ^{3}}{96 x ^{5} + 1200 x ^{4} + 6000 x ^{3} + 15000 x ^{2} + 18750 x + 9375}

求解步骤

\frac{160 x ^{6} + 50000 x ^{3}}{3 ( 2 x + 5 ) ^{5}}

(2 x + 5)^{5} = 32 x^{5} + 400 x^{4} + 2000 x^{3} + 5000 x^{2} + 6250 x + 3125

= \frac{160 x ^{6} + 50000 x ^{3}}{3 ( 32 x ^{5} + 400 x ^{4} + 2000 x ^{3} + 5000 x ^{2} + 6250 x + 3125 )}

乘开

3 (32 x^{5} + 400 x^{4} + 2000 x^{3} + 5000 x^{2} + 6250 x + 3125) : 96 x^{5} + 1200 x^{4} + 6000 x^{3} + 15000 x^{2} + 18750 x + 9375

= \frac{160 x ^{6} + 50000 x ^{3}}{96 x ^{5} + 1200 x ^{4} + 6000 x ^{3} + 15000 x ^{2} + 18750 x + 9375}

e x p an d (- 7 3 x - 9 4 x + 2 x^{4}) d x

e x p an d \frac{( k + 2 ) ( 2 k + 3 ) ( 2 k + 5 )}{3}

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

e x p an d \frac{- 10 ( x + 3 ) ^{\frac{3}{2}} + 2 ( x + 3 ) ^{\frac{5}{2}}}{5}

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