展开 ((2+x)^2(x-6))/(32x^4)

解答

展开

\frac{( 2 + x ) ^{2} ( x - 6 )}{32 x ^{4}}

\frac{1}{32 x} - \frac{1}{16 x ^{2}} - \frac{5}{8 x ^{3}} - \frac{3}{4 x ^{4}}

求解步骤

\frac{( 2 + x ) ^{2} ( x - 6 )}{32 x ^{4}}

(2 + x)^{2} = 4 + 4 x + x^{2}

= \frac{( x ^{2} + 4 x + 4 ) ( x - 6 )}{32 x ^{4}}

乘开

(4 + 4 x + x^{2}) (x - 6) : x^{3} - 2 x^{2} - 20 x - 24

= \frac{x ^{3} - 2 x ^{2} - 20 x - 24}{32 x ^{4}}

使用分式法则:

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

\frac{x ^{3} - 2 x ^{2} - 20 x - 24}{32 x ^{4}} = \frac{x ^{3}}{32 x ^{4}} - \frac{2 x ^{2}}{32 x ^{4}} - \frac{20 x}{32 x ^{4}} - \frac{24}{32 x ^{4}}

= \frac{x ^{3}}{32 x ^{4}} - \frac{2 x ^{2}}{32 x ^{4}} - \frac{20 x}{32 x ^{4}} - \frac{24}{32 x ^{4}}

\frac{x ^{3}}{32 x ^{4}} = \frac{1}{32 x}

\frac{2 x ^{2}}{32 x ^{4}} = \frac{1}{16 x ^{2}}

\frac{20 x}{32 x ^{4}} = \frac{5}{8 x ^{3}}

\frac{24}{32 x ^{4}} = \frac{3}{4 x ^{4}}

= \frac{1}{32 x} - \frac{1}{16 x ^{2}} - \frac{5}{8 x ^{3}} - \frac{3}{4 x ^{4}}

s im pl i f y (3 x^{2} + 4 3 x) (16)

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

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

e x p an d - 2^{6}

e x p an d \frac{( 3 w - 1 ) ( 3 w + 4 )}{( w - 1 ) ( 3 w - 4 )}