展开 ((20+x^2)^2)/9

解答

展开

\frac{( 20 + x ^{2} ) ^{2}}{9}

\frac{x ^{4}}{9} + \frac{40 x ^{2}}{9} + \frac{400}{9}

求解步骤

\frac{( 20 + x ^{2} ) ^{2}}{9}

(20 + x^{2})^{2} = 400 + 40 x^{2} + x^{4}

= \frac{400 + 40 x ^{2} + x ^{4}}{9}

使用分式法则:

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

\frac{400 + 40 x ^{2} + x ^{4}}{9} = \frac{400}{9} + \frac{40 x ^{2}}{9} + \frac{x ^{4}}{9}

= \frac{400}{9} + \frac{40 x ^{2}}{9} + \frac{x ^{4}}{9}

改写为标准形式

= \frac{x ^{4}}{9} + \frac{40 x ^{2}}{9} + \frac{400}{9}

e x p an d (3 x^{2} + y) d x + (x^{2} y - x) d y

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

e x p an d \frac{4 ( 3 ^{n} - 1 )}{3}

e x p an d (3 x^{2} + 5) ln (2)

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