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Popular >

expand ((x^2)/2-2/x)^9

Solution

expand

(\frac{x ^{2}}{2} - \frac{2}{x})^{9}

Solution

\frac{x ^{18}}{512} - \frac{9 x ^{15}}{128} + \frac{9 x ^{12}}{8} - \frac{21 x ^{9}}{2} + 63 x^{6} - 252 x^{3} + 672 - \frac{1152}{x ^{3}} + \frac{1152}{x ^{6}} - \frac{512}{x ^{9}}

Solution steps

(\frac{x ^{2}}{2} - \frac{2}{x})^{9}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = \frac{x ^{2}}{2}, b = - \frac{2}{x}

= i = 0 \sum 9 (i 9) (\frac{x ^{2}}{2})^{(9 - i)} (- \frac{2}{x})^{i}

Expand summation

= \frac{9 !}{0 ! ( 9 - 0 ) !} (\frac{x ^{2}}{2})^{9} (- \frac{2}{x})^{0} + \frac{9 !}{1 ! ( 9 - 1 ) !} (\frac{x ^{2}}{2})^{8} (- \frac{2}{x})^{1} + \frac{9 !}{2 ! ( 9 - 2 ) !} (\frac{x ^{2}}{2})^{7} (- \frac{2}{x})^{2} + \frac{9 !}{3 ! ( 9 - 3 ) !} (\frac{x ^{2}}{2})^{6} (- \frac{2}{x})^{3} + \frac{9 !}{4 ! ( 9 - 4 ) !} (\frac{x ^{2}}{2})^{5} (- \frac{2}{x})^{4} + \frac{9 !}{5 ! ( 9 - 5 ) !} (\frac{x ^{2}}{2})^{4} (- \frac{2}{x})^{5} + \frac{9 !}{6 ! ( 9 - 6 ) !} (\frac{x ^{2}}{2})^{3} (- \frac{2}{x})^{6} + \frac{9 !}{7 ! ( 9 - 7 ) !} (\frac{x ^{2}}{2})^{2} (- \frac{2}{x})^{7} + \frac{9 !}{8 ! ( 9 - 8 ) !} (\frac{x ^{2}}{2})^{1} (- \frac{2}{x})^{8} + \frac{9 !}{9 ! ( 9 - 9 ) !} (\frac{x ^{2}}{2})^{0} (- \frac{2}{x})^{9}

Simplify

\frac{9 !}{0 ! ( 9 - 0 ) !} (\frac{x ^{2}}{2})^{9} (- \frac{2}{x})^{0} : \frac{x ^{18}}{512}

Simplify

\frac{9 !}{1 ! ( 9 - 1 ) !} (\frac{x ^{2}}{2})^{8} (- \frac{2}{x})^{1} : - \frac{9 x ^{15}}{128}

Simplify

\frac{9 !}{2 ! ( 9 - 2 ) !} (\frac{x ^{2}}{2})^{7} (- \frac{2}{x})^{2} : \frac{9 x ^{12}}{8}

Simplify

\frac{9 !}{3 ! ( 9 - 3 ) !} (\frac{x ^{2}}{2})^{6} (- \frac{2}{x})^{3} : - \frac{21 x ^{9}}{2}

Simplify

\frac{9 !}{4 ! ( 9 - 4 ) !} (\frac{x ^{2}}{2})^{5} (- \frac{2}{x})^{4} : 63 x^{6}

Simplify

\frac{9 !}{5 ! ( 9 - 5 ) !} (\frac{x ^{2}}{2})^{4} (- \frac{2}{x})^{5} : - 252 x^{3}

Simplify

\frac{9 !}{6 ! ( 9 - 6 ) !} (\frac{x ^{2}}{2})^{3} (- \frac{2}{x})^{6} : 672

Simplify

\frac{9 !}{7 ! ( 9 - 7 ) !} (\frac{x ^{2}}{2})^{2} (- \frac{2}{x})^{7} : - \frac{1152}{x ^{3}}

Simplify

\frac{9 !}{8 ! ( 9 - 8 ) !} (\frac{x ^{2}}{2})^{1} (- \frac{2}{x})^{8} : \frac{1152}{x ^{6}}

Simplify

\frac{9 !}{9 ! ( 9 - 9 ) !} (\frac{x ^{2}}{2})^{0} (- \frac{2}{x})^{9} : - \frac{512}{x ^{9}}

= \frac{x ^{18}}{512} - \frac{9 x ^{15}}{128} + \frac{9 x ^{12}}{8} - \frac{21 x ^{9}}{2} + 63 x^{6} - 252 x^{3} + 672 - \frac{1152}{x ^{3}} + \frac{1152}{x ^{6}} - \frac{512}{x ^{9}}

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Frequently Asked Questions (FAQ)

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