What is expand (x^2+1/x)^4 ?

The solution to expand (x^2+1/x)^4 is x^8+4x^5+6x^2+4/x+1/(x^4)

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expand (x^2+1/x)^4

expand

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

x^{8} + 4 x^{5} + 6 x^{2} + \frac{4}{x} + \frac{1}{x ^{4}}

Solution steps

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

Apply binomial theorem:

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

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

= i = 0 \sum 4 (i 4) (x^{2})^{(4 - i)} (\frac{1}{x})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (x^{2})^{4} (\frac{1}{x})^{0} : x^{8}

Simplify

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

Simplify

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

Simplify

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

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x^{2})^{0} (\frac{1}{x})^{4} : \frac{1}{x ^{4}}

= x^{8} + 4 x^{5} + 6 x^{2} + \frac{4}{x} + \frac{1}{x ^{4}}

(3 c - 2 d)^{6}

\frac{a}{s ( s + a )}

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

(x - 1)^{3}

(4 x - 5 i)^{2}

What is expand (x^2+1/x)^4 ?
The solution to expand (x^2+1/x)^4 is x^8+4x^5+6x^2+4/x+1/(x^4)