What is expand (1/(x^2)-3x)^5 ?

The solution to expand (1/(x^2)-3x)^5 is 1/(x^{10)}-(15}{x^7}+(90)/(x^4)-\frac{270)/x+405x^2-243x^5

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expand (1/(x^2)-3x)^5

expand

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

\frac{1}{x ^{10}} - \frac{15}{x ^{7}} + \frac{90}{x ^{4}} - \frac{270}{x} + 405 x^{2} - 243 x^{5}

Solution steps

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

Apply binomial theorem:

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

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

= i = 0 \sum 5 (i 5) (\frac{1}{x ^{2}})^{(5 - i)} (- 3 x)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (\frac{1}{x ^{2}})^{5} (- 3 x)^{0} : \frac{1}{x ^{10}}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (\frac{1}{x ^{2}})^{4} (- 3 x)^{1} : - \frac{15}{x ^{7}}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (\frac{1}{x ^{2}})^{3} (- 3 x)^{2} : \frac{90}{x ^{4}}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (\frac{1}{x ^{2}})^{2} (- 3 x)^{3} : - \frac{270}{x}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (\frac{1}{x ^{2}})^{1} (- 3 x)^{4} : 405 x^{2}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (\frac{1}{x ^{2}})^{0} (- 3 x)^{5} : - 243 x^{5}

= \frac{1}{x ^{10}} - \frac{15}{x ^{7}} + \frac{90}{x ^{4}} - \frac{270}{x} + 405 x^{2} - 243 x^{5}

\frac{x - 5}{( x - 1 ) ( x + 4 )}

\frac{1}{( 2 + j w ) ^{2}}

(2 x + (4 x^{2} - 1))^{2}

(2 x^{2} + 6) (3 x^{\frac{1}{2}})

(x^{2 + y^{2}})^{2}

What is expand (1/(x^2)-3x)^5 ?
The solution to expand (1/(x^2)-3x)^5 is 1/(x^{10)}-(15}{x^7}+(90)/(x^4)-\frac{270)/x+405x^2-243x^5