展开 x-1/6 x(x-1)+1/60 x(x-1)(x-4)

解答

展开

x - \frac{1}{6} x (x - 1) + \frac{1}{60} x (x - 1) (x - 4)

\frac{37 x}{30} - \frac{x ^{2}}{4} + \frac{x ^{3}}{60}

求解步骤

x - \frac{1}{6} x (x - 1) + \frac{1}{60} x (x - 1) (x - 4)

展开

- \frac{1}{6} x (x - 1) : - \frac{x ^{2}}{6} + \frac{x}{6}

= x - \frac{x ^{2}}{6} + \frac{x}{6} + \frac{1}{60} x (x - 1) (x - 4)

展开

\frac{1}{60} x (x - 1) (x - 4) : \frac{x ^{3}}{60} - \frac{x ^{2}}{12} + \frac{x}{15}

= x - \frac{x ^{2}}{6} + \frac{x}{6} + \frac{x ^{3}}{60} - \frac{x ^{2}}{12} + \frac{x}{15}

合并

x - \frac{x ^{2}}{6} + \frac{x}{6} + \frac{x ^{3}}{60} - \frac{x ^{2}}{12} + \frac{x}{15} : \frac{37 x}{30} - \frac{x ^{2}}{4} + \frac{x ^{3}}{60}

= \frac{37 x}{30} - \frac{x ^{2}}{4} + \frac{x ^{3}}{60}

s im pl i f y - 2 (sin (2 x) + cos (2 x))

s im pl i f y (x - \frac{1}{4}) (x - \frac{1}{2})

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

s im pl i f y (3 - x - 2)^{2}

e x p an d \frac{( 2 x - 5 ) ^{5}}{( 2 x - 1 ) ^{4}}