展开 (y^8(10y^2-5)^2)/4

解答

展开

\frac{y ^{8} ( 10 y ^{2} - 5 ) ^{2}}{4}

25 y^{12} - 25 y^{10} + \frac{25 y ^{8}}{4}

求解步骤

\frac{y ^{8} ( 10 y ^{2} - 5 ) ^{2}}{4}

(10 y^{2} - 5)^{2} = 100 y^{4} - 100 y^{2} + 25

= \frac{y ^{8} ( 100 y ^{4} - 100 y ^{2} + 25 )}{4}

乘开

y^{8} (100 y^{4} - 100 y^{2} + 25) : 100 y^{12} - 100 y^{10} + 25 y^{8}

= \frac{100 y ^{12} - 100 y ^{10} + 25 y ^{8}}{4}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{100 y ^{12} - 100 y ^{10} + 25 y ^{8}}{4} = \frac{100 y ^{12}}{4} - \frac{100 y ^{10}}{4} + \frac{25 y ^{8}}{4}

= \frac{100 y ^{12}}{4} - \frac{100 y ^{10}}{4} + \frac{25 y ^{8}}{4}

数字相除:

\frac{100}{4} = 25

= 25 y^{12} - 25 y^{10} + \frac{25 y ^{8}}{4}

e x p an d (2 y + x) d x - x d y

\frac{d ^{2}}{d k ^{2}} ((y (k, x)) (e^{6 x} - k x))

s im pl i f y (\frac{i}{n} - 1)^{3}

e x p an d 2 (7 + 11)

e x p an d \frac{1}{( 2 ( n + 1 ) ) !}