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

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

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

expand

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

\frac{x ^{30}}{59049} - \frac{20 x ^{25}}{19683} + \frac{20 x ^{20}}{729} - \frac{320 x ^{15}}{729} + \frac{1120 x ^{10}}{243} - \frac{896 x ^{5}}{27} + \frac{4480}{27} - \frac{5120}{9 x ^{5}} + \frac{1280}{x ^{10}} - \frac{5120}{3 x ^{15}} + \frac{1024}{x ^{20}}

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

\frac{10 !}{0 ! ( 10 - 0 ) !} (\frac{x ^{3}}{3})^{10} (- \frac{2}{x ^{2}})^{0} : \frac{x ^{30}}{59049}

Simplify

\frac{10 !}{1 ! ( 10 - 1 ) !} (\frac{x ^{3}}{3})^{9} (- \frac{2}{x ^{2}})^{1} : - \frac{20 x ^{25}}{19683}

Simplify

\frac{10 !}{2 ! ( 10 - 2 ) !} (\frac{x ^{3}}{3})^{8} (- \frac{2}{x ^{2}})^{2} : \frac{20 x ^{20}}{729}

Simplify

\frac{10 !}{3 ! ( 10 - 3 ) !} (\frac{x ^{3}}{3})^{7} (- \frac{2}{x ^{2}})^{3} : - \frac{320 x ^{15}}{729}

Simplify

\frac{10 !}{4 ! ( 10 - 4 ) !} (\frac{x ^{3}}{3})^{6} (- \frac{2}{x ^{2}})^{4} : \frac{1120 x ^{10}}{243}

Simplify

\frac{10 !}{5 ! ( 10 - 5 ) !} (\frac{x ^{3}}{3})^{5} (- \frac{2}{x ^{2}})^{5} : - \frac{896 x ^{5}}{27}

Simplify

\frac{10 !}{6 ! ( 10 - 6 ) !} (\frac{x ^{3}}{3})^{4} (- \frac{2}{x ^{2}})^{6} : \frac{4480}{27}

Simplify

\frac{10 !}{7 ! ( 10 - 7 ) !} (\frac{x ^{3}}{3})^{3} (- \frac{2}{x ^{2}})^{7} : - \frac{5120}{9 x ^{5}}

Simplify

\frac{10 !}{8 ! ( 10 - 8 ) !} (\frac{x ^{3}}{3})^{2} (- \frac{2}{x ^{2}})^{8} : \frac{1280}{x ^{10}}

Simplify

\frac{10 !}{9 ! ( 10 - 9 ) !} (\frac{x ^{3}}{3})^{1} (- \frac{2}{x ^{2}})^{9} : - \frac{5120}{3 x ^{15}}

Simplify

\frac{10 !}{10 ! ( 10 - 10 ) !} (\frac{x ^{3}}{3})^{0} (- \frac{2}{x ^{2}})^{10} : \frac{1024}{x ^{20}}

= \frac{x ^{30}}{59049} - \frac{20 x ^{25}}{19683} + \frac{20 x ^{20}}{729} - \frac{320 x ^{15}}{729} + \frac{1120 x ^{10}}{243} - \frac{896 x ^{5}}{27} + \frac{4480}{27} - \frac{5120}{9 x ^{5}} + \frac{1280}{x ^{10}} - \frac{5120}{3 x ^{15}} + \frac{1024}{x ^{20}}

\frac{π}{3} ((18 + y) (3 + \frac{y}{6})^{2} - 21 \cdot 3^{2}) y

\frac{5 x ^{2} - 2 x}{3 ( x - 1 ) ( x + 0.4 ) ( x + 1.2 )}

(- 6 e^{- 6 x}) (1 + 6 x)

\frac{2 x - 3}{( x - 1 ) ^{2}}

A (30, - 11) y B (- 7, 22)

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