展开 (5(5t^2-1)^4(100t-5t^2-1))/((10-t)^6)

解答

展开

\frac{5 ( 5 t ^{2} - 1 ) ^{4} ( 100 t - 5 t ^{2} - 1 )}{( 10 - t ) ^{6}}

\frac{- 15625 t ^{10} + 312500 t ^{9} + 9375 t ^{8} - 250000 t ^{7} - 1250 t ^{6} + 75000 t ^{5} - 250 t ^{4} - 10000 t ^{3} + 75 t ^{2} + 500 t - 5}{1000000 - 600000 t + 150000 t ^{2} - 20000 t ^{3} + 1500 t ^{4} - 60 t ^{5} + t ^{6}}

求解步骤

\frac{5 ( 5 t ^{2} - 1 ) ^{4} ( 100 t - 5 t ^{2} - 1 )}{( 10 - t ) ^{6}}

(10 - t)^{6} = 1000000 - 600000 t + 150000 t^{2} - 20000 t^{3} + 1500 t^{4} - 60 t^{5} + t^{6}

= \frac{5 ( 5 t ^{2} - 1 ) ^{4} ( - 5 t ^{2} + 100 t - 1 )}{1000000 - 600000 t + 150000 t ^{2} - 20000 t ^{3} + 1500 t ^{4} - 60 t ^{5} + t ^{6}}

(5 t^{2} - 1)^{4} = 625 t^{8} - 500 t^{6} + 150 t^{4} - 20 t^{2} + 1

= \frac{5 ( 625 t ^{8} - 500 t ^{6} + 150 t ^{4} - 20 t ^{2} + 1 ) ( - 5 t ^{2} + 100 t - 1 )}{1000000 - 600000 t + 150000 t ^{2} - 20000 t ^{3} + 1500 t ^{4} - 60 t ^{5} + t ^{6}}

乘开

5 (625 t^{8} - 500 t^{6} + 150 t^{4} - 20 t^{2} + 1) (100 t - 5 t^{2} - 1) : - 15625 t^{10} + 312500 t^{9} + 9375 t^{8} - 250000 t^{7} - 1250 t^{6} + 75000 t^{5} - 250 t^{4} - 10000 t^{3} + 75 t^{2} + 500 t - 5

= \frac{- 15625 t ^{10} + 312500 t ^{9} + 9375 t ^{8} - 250000 t ^{7} - 1250 t ^{6} + 75000 t ^{5} - 250 t ^{4} - 10000 t ^{3} + 75 t ^{2} + 500 t - 5}{1000000 - 600000 t + 150000 t ^{2} - 20000 t ^{3} + 1500 t ^{4} - 60 t ^{5} + t ^{6}}

e x p an d sin (t) - sin (t) (u) (t - 2 π)

e x p an d 2 cos (2) (x - \frac{π}{3}) - 1

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

e x p an d \frac{1}{x ( x + 5 )}

e x p an d \frac{- a ( b - 2 a ) + 3 c ( - b - 2 a )}{a ( b - 2 a ) + 3 c ( b - 2 a )}