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

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

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

expand

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

x^{30} + 100 x^{25} + 4500 x^{20} + 120000 x^{15} + 2100000 x^{10} + 25200000 x^{5} + 210000000 + \frac{1200000000}{x ^{5}} + \frac{4500000000}{x ^{10}} + \frac{1 0 ^{10}}{x ^{15}} + \frac{1 0 ^{10}}{x ^{20}}

Solution steps

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

Apply binomial theorem:

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

a = x^{3}, b = \frac{10}{x ^{2}}

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

Expand summation

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

Simplify

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

Simplify

\frac{10 !}{1 ! ( 10 - 1 ) !} (x^{3})^{9} (\frac{10}{x ^{2}})^{1} : 100 x^{25}

Simplify

\frac{10 !}{2 ! ( 10 - 2 ) !} (x^{3})^{8} (\frac{10}{x ^{2}})^{2} : 4500 x^{20}

Simplify

\frac{10 !}{3 ! ( 10 - 3 ) !} (x^{3})^{7} (\frac{10}{x ^{2}})^{3} : 120000 x^{15}

Simplify

\frac{10 !}{4 ! ( 10 - 4 ) !} (x^{3})^{6} (\frac{10}{x ^{2}})^{4} : 2100000 x^{10}

Simplify

\frac{10 !}{5 ! ( 10 - 5 ) !} (x^{3})^{5} (\frac{10}{x ^{2}})^{5} : 25200000 x^{5}

Simplify

\frac{10 !}{6 ! ( 10 - 6 ) !} (x^{3})^{4} (\frac{10}{x ^{2}})^{6} : 210000000

Simplify

\frac{10 !}{7 ! ( 10 - 7 ) !} (x^{3})^{3} (\frac{10}{x ^{2}})^{7} : \frac{1200000000}{x ^{5}}

Simplify

\frac{10 !}{8 ! ( 10 - 8 ) !} (x^{3})^{2} (\frac{10}{x ^{2}})^{8} : \frac{4500000000}{x ^{10}}

Simplify

\frac{10 !}{9 ! ( 10 - 9 ) !} (x^{3})^{1} (\frac{10}{x ^{2}})^{9} : \frac{1 0 ^{10}}{x ^{15}}

Simplify

\frac{10 !}{10 ! ( 10 - 10 ) !} (x^{3})^{0} (\frac{10}{x ^{2}})^{10} : \frac{1 0 ^{10}}{x ^{20}}

= x^{30} + 100 x^{25} + 4500 x^{20} + 120000 x^{15} + 2100000 x^{10} + 25200000 x^{5} + 210000000 + \frac{1200000000}{x ^{5}} + \frac{4500000000}{x ^{10}} + \frac{1 0 ^{10}}{x ^{15}} + \frac{1 0 ^{10}}{x ^{20}}

18 (3 sin (x) - 4 sin^{3} (x))

(x - 5 - 2) (x - 5 + 2)

(x - 3) (x + 2) (x - 2) (x - 2) (x + 2)

\frac{( a - 2 ) ( a ^{4} + 2 a ^{3} - 2 a ^{2} - 4 a + 4 )}{( a ^{2} - 2 ) ^{2}}

P (6, - 2) y Q (0, 6)

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