展开 ((6-25x^2)^2)/(900)

解答

展开

\frac{( 6 - 25 x ^{2} ) ^{2}}{900}

\frac{25 x ^{4}}{36} - \frac{x ^{2}}{3} + \frac{1}{25}

求解步骤

\frac{( 6 - 25 x ^{2} ) ^{2}}{900}

(6 - 25 x^{2})^{2} = 36 - 300 x^{2} + 625 x^{4}

= \frac{36 - 300 x ^{2} + 625 x ^{4}}{900}

使用分式法则:

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

\frac{36 - 300 x ^{2} + 625 x ^{4}}{900} = \frac{36}{900} - \frac{300 x ^{2}}{900} + \frac{625 x ^{4}}{900}

= \frac{36}{900} - \frac{300 x ^{2}}{900} + \frac{625 x ^{4}}{900}

消掉

\frac{36}{900} : \frac{1}{25}

= \frac{1}{25} - \frac{300 x ^{2}}{900} + \frac{625 x ^{4}}{900}

消掉

\frac{300 x ^{2}}{900} : \frac{x ^{2}}{3}

= \frac{1}{25} - \frac{x ^{2}}{3} + \frac{625 x ^{4}}{900}

消掉

\frac{625 x ^{4}}{900} : \frac{25 x ^{4}}{36}

= \frac{1}{25} - \frac{x ^{2}}{3} + \frac{25 x ^{4}}{36}

改写为标准形式

= \frac{25 x ^{4}}{36} - \frac{x ^{2}}{3} + \frac{1}{25}

e x p an d \frac{12}{7 ( 2 x - 5 )}

e x p an d \frac{3 ( 5 - y )}{2}

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

e x p an d 10 sin (\frac{π}{50 ( t - 25 )}) + 12

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