What is expand (2x^2-1/x)^6 ?

The solution to expand (2x^2-1/x)^6 is 64x^{12}-192x^9+240x^6-160x^3+60-(12)/(x^3)+1/(x^6)

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expand (2x^2-1/x)^6

expand

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

64 x^{12} - 192 x^{9} + 240 x^{6} - 160 x^{3} + 60 - \frac{12}{x ^{3}} + \frac{1}{x ^{6}}

Solution steps

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

Apply binomial theorem:

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

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

= i = 0 \sum 6 (i 6) (2 x^{2})^{(6 - i)} (- \frac{1}{x})^{i}

Expand summation

= \frac{6 !}{0 ! ( 6 - 0 ) !} (2 x^{2})^{6} (- \frac{1}{x})^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} (2 x^{2})^{5} (- \frac{1}{x})^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} (2 x^{2})^{4} (- \frac{1}{x})^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} (2 x^{2})^{3} (- \frac{1}{x})^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} (2 x^{2})^{2} (- \frac{1}{x})^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} (2 x^{2})^{1} (- \frac{1}{x})^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} (2 x^{2})^{0} (- \frac{1}{x})^{6}

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} (2 x^{2})^{6} (- \frac{1}{x})^{0} : 64 x^{12}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} (2 x^{2})^{5} (- \frac{1}{x})^{1} : - 192 x^{9}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} (2 x^{2})^{4} (- \frac{1}{x})^{2} : 240 x^{6}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} (2 x^{2})^{3} (- \frac{1}{x})^{3} : - 160 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} (2 x^{2})^{2} (- \frac{1}{x})^{4} : 60

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} (2 x^{2})^{1} (- \frac{1}{x})^{5} : - \frac{12}{x ^{3}}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} (2 x^{2})^{0} (- \frac{1}{x})^{6} : \frac{1}{x ^{6}}

= 64 x^{12} - 192 x^{9} + 240 x^{6} - 160 x^{3} + 60 - \frac{12}{x ^{3}} + \frac{1}{x ^{6}}

7 \cdot (9 + 2)

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

\frac{10}{( s + 2 ) ( s + 1 ) ^{3}}

5 (10 + 2)

8 \cdot (\frac{x}{2} + \frac{1}{4})

What is expand (2x^2-1/x)^6 ?
The solution to expand (2x^2-1/x)^6 is 64x^{12}-192x^9+240x^6-160x^3+60-(12)/(x^3)+1/(x^6)