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

The solution to expand (x^2-2/x)^5 is x^{10}-10x^7+40x^4-80x+(80)/(x^2)-(32)/(x^5)

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

expand

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

x^{10} - 10 x^{7} + 40 x^{4} - 80 x + \frac{80}{x ^{2}} - \frac{32}{x ^{5}}

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (x^{2})^{4} (- \frac{2}{x})^{1} : - 10 x^{7}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (x^{2})^{3} (- \frac{2}{x})^{2} : 40 x^{4}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (x^{2})^{2} (- \frac{2}{x})^{3} : - 80 x

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (x^{2})^{1} (- \frac{2}{x})^{4} : \frac{80}{x ^{2}}

Simplify

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

= x^{10} - 10 x^{7} + 40 x^{4} - 80 x + \frac{80}{x ^{2}} - \frac{32}{x ^{5}}

(- 4, - 1) u (- 1, 2)

(x^{5} + \frac{3}{5}) (x^{5} + \frac{1}{10})

lo g_{10} (3) (x + 4)

\frac{( 4 x + 1 ) ( 3 x - 1 )}{6 x ^{2}}

lo g_{10} (3) (x - 6)

What is expand (x^2-2/x)^5 ?
The solution to expand (x^2-2/x)^5 is x^{10}-10x^7+40x^4-80x+(80)/(x^2)-(32)/(x^5)