What is expand (3x^2+1/x)^4 ?

The solution to expand (3x^2+1/x)^4 is 81x^8+108x^5+54x^2+(12)/x+1/(x^4)

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expand (3x^2+1/x)^4

expand

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

81 x^{8} + 108 x^{5} + 54 x^{2} + \frac{12}{x} + \frac{1}{x ^{4}}

Solution steps

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

Apply binomial theorem:

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

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

= i = 0 \sum 4 (i 4) (3 x^{2})^{(4 - i)} (\frac{1}{x})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (3 x^{2})^{4} (\frac{1}{x})^{0} : 81 x^{8}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (3 x^{2})^{3} (\frac{1}{x})^{1} : 108 x^{5}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (3 x^{2})^{2} (\frac{1}{x})^{2} : 54 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (3 x^{2})^{1} (\frac{1}{x})^{3} : \frac{12}{x}

Simplify

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

= 81 x^{8} + 108 x^{5} + 54 x^{2} + \frac{12}{x} + \frac{1}{x ^{4}}

(x^{2} + 4) \cdot x

e f (6 e^{2} - 11)

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

(- 4 x^{3} y^{2}) (3 x^{3} y)

- \frac{4 ( 72 - 5 p ^{2} )}{3}

What is expand (3x^2+1/x)^4 ?
The solution to expand (3x^2+1/x)^4 is 81x^8+108x^5+54x^2+(12)/x+1/(x^4)