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

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

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

expand

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

\frac{1024 x ^{40}}{y ^{10}} - \frac{5120 x ^{35}}{y ^{7}} + \frac{11520 x ^{30}}{y ^{4}} - \frac{15360 x ^{25}}{y} + 13440 x^{20} y^{2} - 8064 x^{15} y^{5} + 3360 x^{10} y^{8} - 960 x^{5} y^{11} + 180 y^{14} - \frac{20 y ^{17}}{x ^{5}} + \frac{y ^{20}}{x ^{10}}

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

\frac{10 !}{0 ! ( 10 - 0 ) !} (\frac{2 x ^{4}}{y})^{10} (- \frac{y ^{2}}{x})^{0} : \frac{1024 x ^{40}}{y ^{10}}

Simplify

\frac{10 !}{1 ! ( 10 - 1 ) !} (\frac{2 x ^{4}}{y})^{9} (- \frac{y ^{2}}{x})^{1} : - \frac{5120 x ^{35}}{y ^{7}}

Simplify

\frac{10 !}{2 ! ( 10 - 2 ) !} (\frac{2 x ^{4}}{y})^{8} (- \frac{y ^{2}}{x})^{2} : \frac{11520 x ^{30}}{y ^{4}}

Simplify

\frac{10 !}{3 ! ( 10 - 3 ) !} (\frac{2 x ^{4}}{y})^{7} (- \frac{y ^{2}}{x})^{3} : - \frac{15360 x ^{25}}{y}

Simplify

\frac{10 !}{4 ! ( 10 - 4 ) !} (\frac{2 x ^{4}}{y})^{6} (- \frac{y ^{2}}{x})^{4} : 13440 x^{20} y^{2}

Simplify

\frac{10 !}{5 ! ( 10 - 5 ) !} (\frac{2 x ^{4}}{y})^{5} (- \frac{y ^{2}}{x})^{5} : - 8064 x^{15} y^{5}

Simplify

\frac{10 !}{6 ! ( 10 - 6 ) !} (\frac{2 x ^{4}}{y})^{4} (- \frac{y ^{2}}{x})^{6} : 3360 x^{10} y^{8}

Simplify

\frac{10 !}{7 ! ( 10 - 7 ) !} (\frac{2 x ^{4}}{y})^{3} (- \frac{y ^{2}}{x})^{7} : - 960 x^{5} y^{11}

Simplify

\frac{10 !}{8 ! ( 10 - 8 ) !} (\frac{2 x ^{4}}{y})^{2} (- \frac{y ^{2}}{x})^{8} : 180 y^{14}

Simplify

\frac{10 !}{9 ! ( 10 - 9 ) !} (\frac{2 x ^{4}}{y})^{1} (- \frac{y ^{2}}{x})^{9} : - \frac{20 y ^{17}}{x ^{5}}

Simplify

\frac{10 !}{10 ! ( 10 - 10 ) !} (\frac{2 x ^{4}}{y})^{0} (- \frac{y ^{2}}{x})^{10} : \frac{y ^{20}}{x ^{10}}

= \frac{1024 x ^{40}}{y ^{10}} - \frac{5120 x ^{35}}{y ^{7}} + \frac{11520 x ^{30}}{y ^{4}} - \frac{15360 x ^{25}}{y} + 13440 x^{20} y^{2} - 8064 x^{15} y^{5} + 3360 x^{10} y^{8} - 960 x^{5} y^{11} + 180 y^{14} - \frac{20 y ^{17}}{x ^{5}} + \frac{y ^{20}}{x ^{10}}

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