What is expand (3x^2-1/(x^3))^{10} ?

The solution to expand (3x^2-1/(x^3))^{10} is

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expand (3x^2-1/(x^3))^{10}

expand

(3 x^{2} - \frac{1}{x ^{3}})^{10}

59049 x^{20} - 196830 x^{15} + 295245 x^{10} - 262440 x^{5} + 153090 - \frac{61236}{x ^{5}} + \frac{17010}{x ^{10}} - \frac{3240}{x ^{15}} + \frac{405}{x ^{20}} - \frac{30}{x ^{25}} + \frac{1}{x ^{30}}

Solution steps

(3 x^{2} - \frac{1}{x ^{3}})^{10}

Apply binomial theorem:

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

a = 3 x^{2}, b = - \frac{1}{x ^{3}}

= i = 0 \sum 10 (i 10) (3 x^{2})^{(10 - i)} (- \frac{1}{x ^{3}})^{i}

Expand summation

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

Simplify

\frac{10 !}{0 ! ( 10 - 0 ) !} (3 x^{2})^{10} (- \frac{1}{x ^{3}})^{0} : 59049 x^{20}

Simplify

\frac{10 !}{1 ! ( 10 - 1 ) !} (3 x^{2})^{9} (- \frac{1}{x ^{3}})^{1} : - 196830 x^{15}

Simplify

\frac{10 !}{2 ! ( 10 - 2 ) !} (3 x^{2})^{8} (- \frac{1}{x ^{3}})^{2} : 295245 x^{10}

Simplify

\frac{10 !}{3 ! ( 10 - 3 ) !} (3 x^{2})^{7} (- \frac{1}{x ^{3}})^{3} : - 262440 x^{5}

Simplify

\frac{10 !}{4 ! ( 10 - 4 ) !} (3 x^{2})^{6} (- \frac{1}{x ^{3}})^{4} : 153090

Simplify

\frac{10 !}{5 ! ( 10 - 5 ) !} (3 x^{2})^{5} (- \frac{1}{x ^{3}})^{5} : - \frac{61236}{x ^{5}}

Simplify

\frac{10 !}{6 ! ( 10 - 6 ) !} (3 x^{2})^{4} (- \frac{1}{x ^{3}})^{6} : \frac{17010}{x ^{10}}

Simplify

\frac{10 !}{7 ! ( 10 - 7 ) !} (3 x^{2})^{3} (- \frac{1}{x ^{3}})^{7} : - \frac{3240}{x ^{15}}

Simplify

\frac{10 !}{8 ! ( 10 - 8 ) !} (3 x^{2})^{2} (- \frac{1}{x ^{3}})^{8} : \frac{405}{x ^{20}}

Simplify

\frac{10 !}{9 ! ( 10 - 9 ) !} (3 x^{2})^{1} (- \frac{1}{x ^{3}})^{9} : - \frac{30}{x ^{25}}

Simplify

\frac{10 !}{10 ! ( 10 - 10 ) !} (3 x^{2})^{0} (- \frac{1}{x ^{3}})^{10} : \frac{1}{x ^{30}}

= 59049 x^{20} - 196830 x^{15} + 295245 x^{10} - 262440 x^{5} + 153090 - \frac{61236}{x ^{5}} + \frac{17010}{x ^{10}} - \frac{3240}{x ^{15}} + \frac{405}{x ^{20}} - \frac{30}{x ^{25}} + \frac{1}{x ^{30}}

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

(\frac{a}{b} + 3)^{2}

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

(7 - t) (7 + t)

(d^{2} + 1) (6 sin (x))

What is expand (3x^2-1/(x^3))^{10} ?
The solution to expand (3x^2-1/(x^3))^{10} is