What is expand ((x^3)/2+3/(x^2))^{10} ?

The solution to expand ((x^3)/2+3/(x^2))^{10} is

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expand ((x^3)/2+3/(x^2))^{10}

expand

(\frac{x ^{3}}{2} + \frac{3}{x ^{2}})^{10}

\frac{x ^{30}}{1024} + \frac{15 x ^{25}}{256} + \frac{405 x ^{20}}{256} + \frac{405 x ^{15}}{16} + \frac{8505 x ^{10}}{32} + \frac{15309 x ^{5}}{8} + \frac{76545}{8} + \frac{32805}{x ^{5}} + \frac{295245}{4 x ^{10}} + \frac{98415}{x ^{15}} + \frac{59049}{x ^{20}}

Solution steps

(\frac{x ^{3}}{2} + \frac{3}{x ^{2}})^{10}

Apply binomial theorem:

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

a = \frac{x ^{3}}{2}, b = \frac{3}{x ^{2}}

= i = 0 \sum 10 (i 10) (\frac{x ^{3}}{2})^{(10 - i)} (\frac{3}{x ^{2}})^{i}

Expand summation

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

Simplify

\frac{10 !}{0 ! ( 10 - 0 ) !} (\frac{x ^{3}}{2})^{10} (\frac{3}{x ^{2}})^{0} : \frac{x ^{30}}{1024}

Simplify

\frac{10 !}{1 ! ( 10 - 1 ) !} (\frac{x ^{3}}{2})^{9} (\frac{3}{x ^{2}})^{1} : \frac{15 x ^{25}}{256}

Simplify

\frac{10 !}{2 ! ( 10 - 2 ) !} (\frac{x ^{3}}{2})^{8} (\frac{3}{x ^{2}})^{2} : \frac{405 x ^{20}}{256}

Simplify

\frac{10 !}{3 ! ( 10 - 3 ) !} (\frac{x ^{3}}{2})^{7} (\frac{3}{x ^{2}})^{3} : \frac{405 x ^{15}}{16}

Simplify

\frac{10 !}{4 ! ( 10 - 4 ) !} (\frac{x ^{3}}{2})^{6} (\frac{3}{x ^{2}})^{4} : \frac{8505 x ^{10}}{32}

Simplify

\frac{10 !}{5 ! ( 10 - 5 ) !} (\frac{x ^{3}}{2})^{5} (\frac{3}{x ^{2}})^{5} : \frac{15309 x ^{5}}{8}

Simplify

\frac{10 !}{6 ! ( 10 - 6 ) !} (\frac{x ^{3}}{2})^{4} (\frac{3}{x ^{2}})^{6} : \frac{76545}{8}

Simplify

\frac{10 !}{7 ! ( 10 - 7 ) !} (\frac{x ^{3}}{2})^{3} (\frac{3}{x ^{2}})^{7} : \frac{32805}{x ^{5}}

Simplify

\frac{10 !}{8 ! ( 10 - 8 ) !} (\frac{x ^{3}}{2})^{2} (\frac{3}{x ^{2}})^{8} : \frac{295245}{4 x ^{10}}

Simplify

\frac{10 !}{9 ! ( 10 - 9 ) !} (\frac{x ^{3}}{2})^{1} (\frac{3}{x ^{2}})^{9} : \frac{98415}{x ^{15}}

Simplify

\frac{10 !}{10 ! ( 10 - 10 ) !} (\frac{x ^{3}}{2})^{0} (\frac{3}{x ^{2}})^{10} : \frac{59049}{x ^{20}}

= \frac{x ^{30}}{1024} + \frac{15 x ^{25}}{256} + \frac{405 x ^{20}}{256} + \frac{405 x ^{15}}{16} + \frac{8505 x ^{10}}{32} + \frac{15309 x ^{5}}{8} + \frac{76545}{8} + \frac{32805}{x ^{5}} + \frac{295245}{4 x ^{10}} + \frac{98415}{x ^{15}} + \frac{59049}{x ^{20}}

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

\frac{7.3 s ( 1 + 467.4 s )}{s ( 1 + 467.4 s ) + 0.342}

(4 cos (x) + 3 sin (x))^{2}

ln (x^{3} y^{2})

(e^{s} - 1 - e^{- s}) \cdot (e^{2 s} - e^{s} - 1)

What is expand ((x^3)/2+3/(x^2))^{10} ?
The solution to expand ((x^3)/2+3/(x^2))^{10} is