pt

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Álgebra >

expandir (2x+1/x)^{12}

Solução

expandir

(2 x + \frac{1}{x})^{12}

Solução

4096 x^{12} + 24576 x^{10} + 67584 x^{8} + 112640 x^{6} + 126720 x^{4} + 101376 x^{2} + 59136 + \frac{25344}{x ^{2}} + \frac{7920}{x ^{4}} + \frac{1760}{x ^{6}} + \frac{264}{x ^{8}} + \frac{24}{x ^{10}} + \frac{1}{x ^{12}}

Passos da solução

(2 x + \frac{1}{x})^{12}

Aplicar o teorema do binômio:

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

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

= i = 0 \sum 12 (i 12) (2 x)^{(12 - i)} (\frac{1}{x})^{i}

Expandir a soma

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

Simplificar

\frac{12 !}{0 ! ( 12 - 0 ) !} (2 x)^{12} (\frac{1}{x})^{0} : 4096 x^{12}

Simplificar

\frac{12 !}{1 ! ( 12 - 1 ) !} (2 x)^{11} (\frac{1}{x})^{1} : 24576 x^{10}

Simplificar

\frac{12 !}{2 ! ( 12 - 2 ) !} (2 x)^{10} (\frac{1}{x})^{2} : 67584 x^{8}

Simplificar

\frac{12 !}{3 ! ( 12 - 3 ) !} (2 x)^{9} (\frac{1}{x})^{3} : 112640 x^{6}

Simplificar

\frac{12 !}{4 ! ( 12 - 4 ) !} (2 x)^{8} (\frac{1}{x})^{4} : 126720 x^{4}

Simplificar

\frac{12 !}{5 ! ( 12 - 5 ) !} (2 x)^{7} (\frac{1}{x})^{5} : 101376 x^{2}

Simplificar

\frac{12 !}{6 ! ( 12 - 6 ) !} (2 x)^{6} (\frac{1}{x})^{6} : 59136

Simplificar

\frac{12 !}{7 ! ( 12 - 7 ) !} (2 x)^{5} (\frac{1}{x})^{7} : \frac{25344}{x ^{2}}

Simplificar

\frac{12 !}{8 ! ( 12 - 8 ) !} (2 x)^{4} (\frac{1}{x})^{8} : \frac{7920}{x ^{4}}

Simplificar

\frac{12 !}{9 ! ( 12 - 9 ) !} (2 x)^{3} (\frac{1}{x})^{9} : \frac{1760}{x ^{6}}

Simplificar

\frac{12 !}{10 ! ( 12 - 10 ) !} (2 x)^{2} (\frac{1}{x})^{10} : \frac{264}{x ^{8}}

Simplificar

\frac{12 !}{11 ! ( 12 - 11 ) !} (2 x)^{1} (\frac{1}{x})^{11} : \frac{24}{x ^{10}}

Simplificar

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

= 4096 x^{12} + 24576 x^{10} + 67584 x^{8} + 112640 x^{6} + 126720 x^{4} + 101376 x^{2} + 59136 + \frac{25344}{x ^{2}} + \frac{7920}{x ^{4}} + \frac{1760}{x ^{6}} + \frac{264}{x ^{8}} + \frac{24}{x ^{10}} + \frac{1}{x ^{12}}

Exemplos populares

expandir 1/(s(1-e^{-s))}

e x p an d \frac{1}{s ( 1 - e ^{- s} )}

expandir (7s+2)/((s+2)(s-1)(s-2))

e x p an d \frac{7 s + 2}{( s + 2 ) ( s - 1 ) ( s - 2 )}

expandir \sqrt[3]{9}(3\sqrt[3]{3}-2\sqrt[3]{2})

e x p an d 39 (333 - 232)

simplificar ((3x^2)/(2y)+z/6)((3x^2)/(2y)-z/6)

s im pl i f y (\frac{3 x ^{2}}{2 y} + \frac{z}{6}) (\frac{3 x ^{2}}{2 y} - \frac{z}{6})

expandir 2(x+Δx)^3

e x p an d 2 (x + Δ x)^{3}