What is expand (x^2-3/x)^6 ?

The solution to expand (x^2-3/x)^6 is x^{12}-18x^9+135x^6-540x^3+1215-(1458)/(x^3)+(729)/(x^6)

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expand (x^2-3/x)^6

expand

(x^{2} - \frac{3}{x})^{6}

x^{12} - 18 x^{9} + 135 x^{6} - 540 x^{3} + 1215 - \frac{1458}{x ^{3}} + \frac{729}{x ^{6}}

Solution steps

(x^{2} - \frac{3}{x})^{6}

Apply binomial theorem:

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

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

= i = 0 \sum 6 (i 6) (x^{2})^{(6 - i)} (- \frac{3}{x})^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} (x^{2})^{6} (- \frac{3}{x})^{0} : x^{12}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} (x^{2})^{5} (- \frac{3}{x})^{1} : - 18 x^{9}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} (x^{2})^{4} (- \frac{3}{x})^{2} : 135 x^{6}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} (x^{2})^{3} (- \frac{3}{x})^{3} : - 540 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} (x^{2})^{2} (- \frac{3}{x})^{4} : 1215

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} (x^{2})^{1} (- \frac{3}{x})^{5} : - \frac{1458}{x ^{3}}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} (x^{2})^{0} (- \frac{3}{x})^{6} : \frac{729}{x ^{6}}

= x^{12} - 18 x^{9} + 135 x^{6} - 540 x^{3} + 1215 - \frac{1458}{x ^{3}} + \frac{729}{x ^{6}}

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What is expand (x^2-3/x)^6 ?
The solution to expand (x^2-3/x)^6 is x^{12}-18x^9+135x^6-540x^3+1215-(1458)/(x^3)+(729)/(x^6)