What is expand (5/4 x^2-1/(2x))^{10} ?

The solution to expand (5/4 x^2-1/(2x))^{10} is

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expand (5/4 x^2-1/(2x))^{10}

expand

(\frac{5}{4} x^{2} - \frac{1}{2 x})^{10}

\frac{9765625 x ^{20}}{1048576} - \frac{9765625 x ^{17}}{262144} + \frac{17578125 x ^{14}}{262144} - \frac{1171875 x ^{11}}{16384} + \frac{1640625 x ^{8}}{32768} - \frac{196875 x ^{5}}{8192} + \frac{65625 x ^{2}}{8192} - \frac{1875}{1024 x} + \frac{1125}{4096 x ^{4}} - \frac{25}{1024 x ^{7}} + \frac{1}{1024 x ^{10}}

Solution steps

(\frac{5}{4} x^{2} - \frac{1}{2 x})^{10}

Apply binomial theorem:

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

a = \frac{5}{4} x^{2}, b = - \frac{1}{2 x}

= i = 0 \sum 10 (i 10) (\frac{5}{4} x^{2})^{(10 - i)} (- \frac{1}{2 x})^{i}

Expand summation

= \frac{10 !}{0 ! ( 10 - 0 ) !} (\frac{5}{4} x^{2})^{10} (- \frac{1}{2 x})^{0} + \frac{10 !}{1 ! ( 10 - 1 ) !} (\frac{5}{4} x^{2})^{9} (- \frac{1}{2 x})^{1} + \frac{10 !}{2 ! ( 10 - 2 ) !} (\frac{5}{4} x^{2})^{8} (- \frac{1}{2 x})^{2} + \frac{10 !}{3 ! ( 10 - 3 ) !} (\frac{5}{4} x^{2})^{7} (- \frac{1}{2 x})^{3} + \frac{10 !}{4 ! ( 10 - 4 ) !} (\frac{5}{4} x^{2})^{6} (- \frac{1}{2 x})^{4} + \frac{10 !}{5 ! ( 10 - 5 ) !} (\frac{5}{4} x^{2})^{5} (- \frac{1}{2 x})^{5} + \frac{10 !}{6 ! ( 10 - 6 ) !} (\frac{5}{4} x^{2})^{4} (- \frac{1}{2 x})^{6} + \frac{10 !}{7 ! ( 10 - 7 ) !} (\frac{5}{4} x^{2})^{3} (- \frac{1}{2 x})^{7} + \frac{10 !}{8 ! ( 10 - 8 ) !} (\frac{5}{4} x^{2})^{2} (- \frac{1}{2 x})^{8} + \frac{10 !}{9 ! ( 10 - 9 ) !} (\frac{5}{4} x^{2})^{1} (- \frac{1}{2 x})^{9} + \frac{10 !}{10 ! ( 10 - 10 ) !} (\frac{5}{4} x^{2})^{0} (- \frac{1}{2 x})^{10}

Simplify

\frac{10 !}{0 ! ( 10 - 0 ) !} (\frac{5}{4} x^{2})^{10} (- \frac{1}{2 x})^{0} : \frac{9765625 x ^{20}}{1048576}

Simplify

\frac{10 !}{1 ! ( 10 - 1 ) !} (\frac{5}{4} x^{2})^{9} (- \frac{1}{2 x})^{1} : - \frac{9765625 x ^{17}}{262144}

Simplify

\frac{10 !}{2 ! ( 10 - 2 ) !} (\frac{5}{4} x^{2})^{8} (- \frac{1}{2 x})^{2} : \frac{17578125 x ^{14}}{262144}

Simplify

\frac{10 !}{3 ! ( 10 - 3 ) !} (\frac{5}{4} x^{2})^{7} (- \frac{1}{2 x})^{3} : - \frac{1171875 x ^{11}}{16384}

Simplify

\frac{10 !}{4 ! ( 10 - 4 ) !} (\frac{5}{4} x^{2})^{6} (- \frac{1}{2 x})^{4} : \frac{1640625 x ^{8}}{32768}

Simplify

\frac{10 !}{5 ! ( 10 - 5 ) !} (\frac{5}{4} x^{2})^{5} (- \frac{1}{2 x})^{5} : - \frac{196875 x ^{5}}{8192}

Simplify

\frac{10 !}{6 ! ( 10 - 6 ) !} (\frac{5}{4} x^{2})^{4} (- \frac{1}{2 x})^{6} : \frac{65625 x ^{2}}{8192}

Simplify

\frac{10 !}{7 ! ( 10 - 7 ) !} (\frac{5}{4} x^{2})^{3} (- \frac{1}{2 x})^{7} : - \frac{1875}{1024 x}

Simplify

\frac{10 !}{8 ! ( 10 - 8 ) !} (\frac{5}{4} x^{2})^{2} (- \frac{1}{2 x})^{8} : \frac{1125}{4096 x ^{4}}

Simplify

\frac{10 !}{9 ! ( 10 - 9 ) !} (\frac{5}{4} x^{2})^{1} (- \frac{1}{2 x})^{9} : - \frac{25}{1024 x ^{7}}

Simplify

\frac{10 !}{10 ! ( 10 - 10 ) !} (\frac{5}{4} x^{2})^{0} (- \frac{1}{2 x})^{10} : \frac{1}{1024 x ^{10}}

= \frac{9765625 x ^{20}}{1048576} - \frac{9765625 x ^{17}}{262144} + \frac{17578125 x ^{14}}{262144} - \frac{1171875 x ^{11}}{16384} + \frac{1640625 x ^{8}}{32768} - \frac{196875 x ^{5}}{8192} + \frac{65625 x ^{2}}{8192} - \frac{1875}{1024 x} + \frac{1125}{4096 x ^{4}} - \frac{25}{1024 x ^{7}} + \frac{1}{1024 x ^{10}}

(e - 1) \cdot π

tan^{2} (θ) \times (cot^{2} (θ) - cos^{2} (θ))

\frac{( k ( 3 k - 1 ) )}{2}

A (2, 4) y B (- 3, - 5)

\frac{s ^{3} - 5 s ^{2} + 2 s - 5}{( s ^{2} + 1 ) ( s ^{2} - 5 s + 2 )}

What is expand (5/4 x^2-1/(2x))^{10} ?
The solution to expand (5/4 x^2-1/(2x))^{10} is