es

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Álgebra >

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

Solución

desarrollar

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

Solución

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}}

Pasos de solución

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

Aplicar el teorema del binomio:

(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}

Expandir sumatorio

= \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}

Simplificar

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

Simplificar

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

Simplificar

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

Simplificar

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

Simplificar

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

Simplificar

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

Simplificar

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

Simplificar

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

Simplificar

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

Simplificar

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

Simplificar

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

Simplificar

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

Simplificar

\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}}

Ejemplos populares

desarrollar-(sec^2(x/2))/((tan(x/2)-1)^2)

e x p an d - \frac{sec ^{2} ( \frac{x}{2} )}{( tan ( \frac{x}{2} ) - 1 ) ^{2}}

desarrollar-1/8 (36x-16y)

e x p an d - \frac{1}{8} (36 x - 16 y)

desarrollar (x^2-9)/(x(x^2+1))

e x p an d \frac{x ^{2} - 9}{x ( x ^{2} + 1 )}

desarrollar (z^2(a)+z(b)+c)*(z^2(d)+z(e)+f)

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

simplificar (x+10/3)(x+10)

s im pl i f y (x + \frac{10}{3}) (x + 10)