展开 x^{2/5}(y^{1/2}+2x^{6/5})^6

解答

展开

x^{\frac{2}{5}} (y^{\frac{1}{2}} + 2 x^{\frac{6}{5}})^{6}

x^{\frac{2}{5}} y^{3} + 12 x^{\frac{8}{5}} y^{\frac{5}{2}} + 60 x^{\frac{14}{5}} y^{2} + 160 x^{4} y^{\frac{3}{2}} + 240 x^{\frac{26}{5}} y + 192 x^{\frac{32}{5}} y^{\frac{1}{2}} + 64 x^{\frac{38}{5}}

求解步骤

x^{\frac{2}{5}} (y^{\frac{1}{2}} + 2 x^{\frac{6}{5}})^{6}

展开

(y^{\frac{1}{2}} + 2 x^{\frac{6}{5}})^{6} : y^{3} + 12 x^{\frac{6}{5}} y^{\frac{5}{2}} + 60 y^{2} x^{\frac{12}{5}} + 160 x^{\frac{18}{5}} y^{\frac{3}{2}} + 240 y x^{\frac{24}{5}} + 192 x^{6} y^{\frac{1}{2}} + 64 x^{\frac{36}{5}}

= x^{\frac{2}{5}} (y^{3} + 12 x^{\frac{6}{5}} y^{\frac{5}{2}} + 60 y^{2} x^{\frac{12}{5}} + 160 x^{\frac{18}{5}} y^{\frac{3}{2}} + 240 y x^{\frac{24}{5}} + 192 x^{6} y^{\frac{1}{2}} + 64 x^{\frac{36}{5}})

打开括号

= x^{\frac{2}{5}} y^{3} + x^{\frac{2}{5}} \cdot 12 x^{\frac{6}{5}} y^{\frac{5}{2}} + x^{\frac{2}{5}} \cdot 60 y^{2} x^{\frac{12}{5}} + x^{\frac{2}{5}} \cdot 160 x^{\frac{18}{5}} y^{\frac{3}{2}} + x^{\frac{2}{5}} \cdot 240 y x^{\frac{24}{5}} + x^{\frac{2}{5}} \cdot 192 x^{6} y^{\frac{1}{2}} + x^{\frac{2}{5}} \cdot 64 x^{\frac{36}{5}}

x^{\frac{2}{5}} \cdot 12 x^{\frac{6}{5}} y^{\frac{5}{2}} = 12 x^{\frac{8}{5}} y^{\frac{5}{2}}

x^{\frac{2}{5}} \cdot 60 y^{2} x^{\frac{12}{5}} = 60 x^{\frac{14}{5}} y^{2}

x^{\frac{2}{5}} \cdot 160 x^{\frac{18}{5}} y^{\frac{3}{2}} = 160 x^{4} y^{\frac{3}{2}}

x^{\frac{2}{5}} \cdot 240 y x^{\frac{24}{5}} = 240 x^{\frac{26}{5}} y

x^{\frac{2}{5}} \cdot 192 x^{6} y^{\frac{1}{2}} = 192 x^{\frac{32}{5}} y^{\frac{1}{2}}

x^{\frac{2}{5}} \cdot 64 x^{\frac{36}{5}} = 64 x^{\frac{38}{5}}

= x^{\frac{2}{5}} y^{3} + 12 x^{\frac{8}{5}} y^{\frac{5}{2}} + 60 x^{\frac{14}{5}} y^{2} + 160 x^{4} y^{\frac{3}{2}} + 240 x^{\frac{26}{5}} y + 192 x^{\frac{32}{5}} y^{\frac{1}{2}} + 64 x^{\frac{38}{5}}

e x p an d \frac{( x ^{2} + x - 125 ) ( x - 5 )}{( x + 4 ) ( x ^{2} - 9 )}

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

s im pl i f y \frac{1}{( x - 2 i ) ^{2}} + \frac{1}{( x + 2 i ) ^{2}}

s im pl i f y x y (\frac{40 x ^{2} y + 15 x ^{2} + 12 y - 10}{60} + 1)

e x p an d \frac{( x ^{3} + 2 a ) ^{6}}{64 x ^{6}}