展开 (8x^3-5x)^3(sqrt(x)-2x)

解答

展开

(8 x^{3} - 5 x)^{3} (x - 2 x)

512 x^{9} x - 1024 x^{10} - 960 x^{7} x + 1920 x^{8} + 600 x^{5} x - 1200 x^{6} - 125 x^{3} x + 250 x^{4}

求解步骤

(8 x^{3} - 5 x)^{3} (x - 2 x)

展开

(8 x^{3} - 5 x)^{3} : 512 x^{9} - 960 x^{7} + 600 x^{5} - 125 x^{3}

= (512 x^{9} - 960 x^{7} + 600 x^{5} - 125 x^{3}) (x - 2 x)

打开括号

= 512 x^{9} x + 512 x^{9} (- 2 x) - 960 x^{7} x - 960 x^{7} (- 2 x) + 600 x^{5} x + 600 x^{5} (- 2 x) - 125 x^{3} x - 125 x^{3} (- 2 x)

化简

512 x^{9} x + 512 x^{9} (- 2 x) - 960 x^{7} x - 960 x^{7} (- 2 x) + 600 x^{5} x + 600 x^{5} (- 2 x) - 125 x^{3} x - 125 x^{3} (- 2 x) : 512 x^{9} x - 1024 x^{10} - 960 x^{7} x + 1920 x^{8} + 600 x^{5} x - 1200 x^{6} - 125 x^{3} x + 250 x^{4}

= 512 x^{9} x - 1024 x^{10} - 960 x^{7} x + 1920 x^{8} + 600 x^{5} x - 1200 x^{6} - 125 x^{3} x + 250 x^{4}

e x p an d (x^{2} + y^{2}) d x + (x^{2} - x y) d y

e x p an d (3 + 5 i)^{4}

e x p an d (1 - \frac{5}{p})^{3}

e x p an d - e (- e - e^{2})

e x p an d - \frac{20 s}{( s ^{2} + 25 ) ^{2}}