What is expand (3x-2/x)^5 ?

The solution to expand (3x-2/x)^5 is 243x^5-810x^3+1080x-(720)/x+(240)/(x^3)-(32)/(x^5)

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expand (3x-2/x)^5

expand

(3 x - \frac{2}{x})^{5}

243 x^{5} - 810 x^{3} + 1080 x - \frac{720}{x} + \frac{240}{x ^{3}} - \frac{32}{x ^{5}}

Solution steps

(3 x - \frac{2}{x})^{5}

Apply binomial theorem:

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

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

= i = 0 \sum 5 (i 5) (3 x)^{(5 - i)} (- \frac{2}{x})^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (3 x)^{5} (- \frac{2}{x})^{0} : 243 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (3 x)^{4} (- \frac{2}{x})^{1} : - 810 x^{3}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (3 x)^{3} (- \frac{2}{x})^{2} : 1080 x

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (3 x)^{2} (- \frac{2}{x})^{3} : - \frac{720}{x}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (3 x)^{1} (- \frac{2}{x})^{4} : \frac{240}{x ^{3}}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (3 x)^{0} (- \frac{2}{x})^{5} : - \frac{32}{x ^{5}}

= 243 x^{5} - 810 x^{3} + 1080 x - \frac{720}{x} + \frac{240}{x ^{3}} - \frac{32}{x ^{5}}

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(1 + \frac{2}{3} x)^{7} (3 + 7 x)^{2}

What is expand (3x-2/x)^5 ?
The solution to expand (3x-2/x)^5 is 243x^5-810x^3+1080x-(720)/x+(240)/(x^3)-(32)/(x^5)