展开 (45(x-2)^8)/((2x+1)^{10)}

解答

展开

\frac{45 ( x - 2 ) ^{8}}{( 2 x + 1 ) ^{10}}

\frac{45 x ^{8} - 720 x ^{7} + 5040 x ^{6} - 20160 x ^{5} + 50400 x ^{4} - 80640 x ^{3} + 80640 x ^{2} - 46080 x + 11520}{1024 x ^{10} + 5120 x ^{9} + 11520 x ^{8} + 15360 x ^{7} + 13440 x ^{6} + 8064 x ^{5} + 3360 x ^{4} + 960 x ^{3} + 180 x ^{2} + 20 x + 1}

求解步骤

\frac{45 ( x - 2 ) ^{8}}{( 2 x + 1 ) ^{10}}

(2 x + 1)^{10} = 1024 x^{10} + 5120 x^{9} + 11520 x^{8} + 15360 x^{7} + 13440 x^{6} + 8064 x^{5} + 3360 x^{4} + 960 x^{3} + 180 x^{2} + 20 x + 1

= \frac{45 ( x - 2 ) ^{8}}{1024 x ^{10} + 5120 x ^{9} + 11520 x ^{8} + 15360 x ^{7} + 13440 x ^{6} + 8064 x ^{5} + 3360 x ^{4} + 960 x ^{3} + 180 x ^{2} + 20 x + 1}

(x - 2)^{8} = x^{8} - 16 x^{7} + 112 x^{6} - 448 x^{5} + 1120 x^{4} - 1792 x^{3} + 1792 x^{2} - 1024 x + 256

= \frac{45 ( x ^{8} - 16 x ^{7} + 112 x ^{6} - 448 x ^{5} + 1120 x ^{4} - 1792 x ^{3} + 1792 x ^{2} - 1024 x + 256 )}{1024 x ^{10} + 5120 x ^{9} + 11520 x ^{8} + 15360 x ^{7} + 13440 x ^{6} + 8064 x ^{5} + 3360 x ^{4} + 960 x ^{3} + 180 x ^{2} + 20 x + 1}

乘开

45 (x^{8} - 16 x^{7} + 112 x^{6} - 448 x^{5} + 1120 x^{4} - 1792 x^{3} + 1792 x^{2} - 1024 x + 256) : 45 x^{8} - 720 x^{7} + 5040 x^{6} - 20160 x^{5} + 50400 x^{4} - 80640 x^{3} + 80640 x^{2} - 46080 x + 11520

= \frac{45 x ^{8} - 720 x ^{7} + 5040 x ^{6} - 20160 x ^{5} + 50400 x ^{4} - 80640 x ^{3} + 80640 x ^{2} - 46080 x + 11520}{1024 x ^{10} + 5120 x ^{9} + 11520 x ^{8} + 15360 x ^{7} + 13440 x ^{6} + 8064 x ^{5} + 3360 x ^{4} + 960 x ^{3} + 180 x ^{2} + 20 x + 1}

e x p an d \frac{c ab e ^{- b t}}{( 1 + a e ^{- b t} ) ^{2}}

e x p an d 1 + cot^{2} (x)

e x p an d 10 (3 x + 7)

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

e x p an d 2 (x - 7 = - 2 x - 6)