What is expand (4x^2-3/(2x))^{12} ?

The solution to expand (4x^2-3/(2x))^{12} is

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expand (4x^2-3/(2x))^{12}

expand

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

16777216 x^{24} - 75497472 x^{21} + 155713536 x^{18} - 194641920 x^{15} + 164229120 x^{12} - 98537472 x^{9} + 43110144 x^{6} - 13856832 x^{3} + 3247695 - \frac{1082565}{2 x ^{3}} + \frac{1948617}{32 x ^{6}} - \frac{531441}{128 x ^{9}} + \frac{531441}{4096 x ^{12}}

Solution steps

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

Apply binomial theorem:

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

a = 4 x^{2}, b = - \frac{3}{2 x}

= i = 0 \sum 12 (i 12) (4 x^{2})^{(12 - i)} (- \frac{3}{2 x})^{i}

Expand summation

= \frac{12 !}{0 ! ( 12 - 0 ) !} (4 x^{2})^{12} (- \frac{3}{2 x})^{0} + \frac{12 !}{1 ! ( 12 - 1 ) !} (4 x^{2})^{11} (- \frac{3}{2 x})^{1} + \frac{12 !}{2 ! ( 12 - 2 ) !} (4 x^{2})^{10} (- \frac{3}{2 x})^{2} + \frac{12 !}{3 ! ( 12 - 3 ) !} (4 x^{2})^{9} (- \frac{3}{2 x})^{3} + \frac{12 !}{4 ! ( 12 - 4 ) !} (4 x^{2})^{8} (- \frac{3}{2 x})^{4} + \frac{12 !}{5 ! ( 12 - 5 ) !} (4 x^{2})^{7} (- \frac{3}{2 x})^{5} + \frac{12 !}{6 ! ( 12 - 6 ) !} (4 x^{2})^{6} (- \frac{3}{2 x})^{6} + \frac{12 !}{7 ! ( 12 - 7 ) !} (4 x^{2})^{5} (- \frac{3}{2 x})^{7} + \frac{12 !}{8 ! ( 12 - 8 ) !} (4 x^{2})^{4} (- \frac{3}{2 x})^{8} + \frac{12 !}{9 ! ( 12 - 9 ) !} (4 x^{2})^{3} (- \frac{3}{2 x})^{9} + \frac{12 !}{10 ! ( 12 - 10 ) !} (4 x^{2})^{2} (- \frac{3}{2 x})^{10} + \frac{12 !}{11 ! ( 12 - 11 ) !} (4 x^{2})^{1} (- \frac{3}{2 x})^{11} + \frac{12 !}{12 ! ( 12 - 12 ) !} (4 x^{2})^{0} (- \frac{3}{2 x})^{12}

Simplify

\frac{12 !}{0 ! ( 12 - 0 ) !} (4 x^{2})^{12} (- \frac{3}{2 x})^{0} : 16777216 x^{24}

Simplify

\frac{12 !}{1 ! ( 12 - 1 ) !} (4 x^{2})^{11} (- \frac{3}{2 x})^{1} : - 75497472 x^{21}

Simplify

\frac{12 !}{2 ! ( 12 - 2 ) !} (4 x^{2})^{10} (- \frac{3}{2 x})^{2} : 155713536 x^{18}

Simplify

\frac{12 !}{3 ! ( 12 - 3 ) !} (4 x^{2})^{9} (- \frac{3}{2 x})^{3} : - 194641920 x^{15}

Simplify

\frac{12 !}{4 ! ( 12 - 4 ) !} (4 x^{2})^{8} (- \frac{3}{2 x})^{4} : 164229120 x^{12}

Simplify

\frac{12 !}{5 ! ( 12 - 5 ) !} (4 x^{2})^{7} (- \frac{3}{2 x})^{5} : - 98537472 x^{9}

Simplify

\frac{12 !}{6 ! ( 12 - 6 ) !} (4 x^{2})^{6} (- \frac{3}{2 x})^{6} : 43110144 x^{6}

Simplify

\frac{12 !}{7 ! ( 12 - 7 ) !} (4 x^{2})^{5} (- \frac{3}{2 x})^{7} : - 13856832 x^{3}

Simplify

\frac{12 !}{8 ! ( 12 - 8 ) !} (4 x^{2})^{4} (- \frac{3}{2 x})^{8} : 3247695

Simplify

\frac{12 !}{9 ! ( 12 - 9 ) !} (4 x^{2})^{3} (- \frac{3}{2 x})^{9} : - \frac{1082565}{2 x ^{3}}

Simplify

\frac{12 !}{10 ! ( 12 - 10 ) !} (4 x^{2})^{2} (- \frac{3}{2 x})^{10} : \frac{1948617}{32 x ^{6}}

Simplify

\frac{12 !}{11 ! ( 12 - 11 ) !} (4 x^{2})^{1} (- \frac{3}{2 x})^{11} : - \frac{531441}{128 x ^{9}}

Simplify

\frac{12 !}{12 ! ( 12 - 12 ) !} (4 x^{2})^{0} (- \frac{3}{2 x})^{12} : \frac{531441}{4096 x ^{12}}

= 16777216 x^{24} - 75497472 x^{21} + 155713536 x^{18} - 194641920 x^{15} + 164229120 x^{12} - 98537472 x^{9} + 43110144 x^{6} - 13856832 x^{3} + 3247695 - \frac{1082565}{2 x ^{3}} + \frac{1948617}{32 x ^{6}} - \frac{531441}{128 x ^{9}} + \frac{531441}{4096 x ^{12}}

- \frac{sec ^{2} ( \frac{x}{2} )}{( tan ( \frac{x}{2} ) - 1 ) ^{2}}

- \frac{1}{8} (36 x - 16 y)

x \cdot (1 - x - y) \cdot e^{y}

\frac{x ^{2} - 9}{x ( x ^{2} + 1 )}

(z^{2} (a) + z (b) + c) \cdot (z^{2} (d) + z (e) + f)

What is expand (4x^2-3/(2x))^{12} ?
The solution to expand (4x^2-3/(2x))^{12} is