expand ((2-3x^2)^5)/(5x)

פתרון

expand

\frac{( 2 - 3 x ^{2} ) ^{5}}{5 x}

\frac{32}{5 x} - 48 x + 144 x^{3} - 216 x^{5} + 162 x^{7} - \frac{243 x ^{9}}{5}

צעדי פתרון

\frac{( 2 - 3 x ^{2} ) ^{5}}{5 x}

(2 - 3 x^{2})^{5} = 32 - 240 x^{2} + 720 x^{4} - 1080 x^{6} + 810 x^{8} - 243 x^{10}

= \frac{32 - 240 x ^{2} + 720 x ^{4} - 1080 x ^{6} + 810 x ^{8} - 243 x ^{10}}{5 x}

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

: השתמש בתכונת השברים הבאה

\frac{32 - 240 x ^{2} + 720 x ^{4} - 1080 x ^{6} + 810 x ^{8} - 243 x ^{10}}{5 x} = \frac{32}{5 x} - \frac{240 x ^{2}}{5 x} + \frac{720 x ^{4}}{5 x} - \frac{1080 x ^{6}}{5 x} + \frac{810 x ^{8}}{5 x} - \frac{243 x ^{10}}{5 x}

= \frac{32}{5 x} - \frac{240 x ^{2}}{5 x} + \frac{720 x ^{4}}{5 x} - \frac{1080 x ^{6}}{5 x} + \frac{810 x ^{8}}{5 x} - \frac{243 x ^{10}}{5 x}

\frac{240 x ^{2}}{5 x} = 48 x

\frac{720 x ^{4}}{5 x} = 144 x^{3}

\frac{1080 x ^{6}}{5 x} = 216 x^{5}

\frac{810 x ^{8}}{5 x} = 162 x^{7}

\frac{243 x ^{10}}{5 x} = \frac{243 x ^{9}}{5}

= \frac{32}{5 x} - 48 x + 144 x^{3} - 216 x^{5} + 162 x^{7} - \frac{243 x ^{9}}{5}

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