pt

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Álgebra >

expandir (2x-3)^{10}

Solução

expandir

(2 x - 3)^{10}

Solução

1024 x^{10} - 15360 x^{9} + 103680 x^{8} - 414720 x^{7} + 1088640 x^{6} - 1959552 x^{5} + 2449440 x^{4} - 2099520 x^{3} + 1180980 x^{2} - 393660 x + 59049

Passos da solução

(2 x - 3)^{10}

Aplicar o teorema do binômio:

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

a = 2 x, b = - 3

= i = 0 \sum 10 (i 10) (2 x)^{(10 - i)} (- 3)^{i}

Expandir a soma

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

Simplificar

\frac{10 !}{0 ! ( 10 - 0 ) !} (2 x)^{10} (- 3)^{0} : 1024 x^{10}

Simplificar

\frac{10 !}{1 ! ( 10 - 1 ) !} (2 x)^{9} (- 3)^{1} : - 15360 x^{9}

Simplificar

\frac{10 !}{2 ! ( 10 - 2 ) !} (2 x)^{8} (- 3)^{2} : 103680 x^{8}

Simplificar

\frac{10 !}{3 ! ( 10 - 3 ) !} (2 x)^{7} (- 3)^{3} : - 414720 x^{7}

Simplificar

\frac{10 !}{4 ! ( 10 - 4 ) !} (2 x)^{6} (- 3)^{4} : 1088640 x^{6}

Simplificar

\frac{10 !}{5 ! ( 10 - 5 ) !} (2 x)^{5} (- 3)^{5} : - 1959552 x^{5}

Simplificar

\frac{10 !}{6 ! ( 10 - 6 ) !} (2 x)^{4} (- 3)^{6} : 2449440 x^{4}

Simplificar

\frac{10 !}{7 ! ( 10 - 7 ) !} (2 x)^{3} (- 3)^{7} : - 2099520 x^{3}

Simplificar

\frac{10 !}{8 ! ( 10 - 8 ) !} (2 x)^{2} (- 3)^{8} : 1180980 x^{2}

Simplificar

\frac{10 !}{9 ! ( 10 - 9 ) !} (2 x)^{1} (- 3)^{9} : - 393660 x

Simplificar

\frac{10 !}{10 ! ( 10 - 10 ) !} (2 x)^{0} (- 3)^{10} : 59049

= 1024 x^{10} - 15360 x^{9} + 103680 x^{8} - 414720 x^{7} + 1088640 x^{6} - 1959552 x^{5} + 2449440 x^{4} - 2099520 x^{3} + 1180980 x^{2} - 393660 x + 59049

Exemplos populares

simplificar-7*(-5)

s im pl i f y - 7 \cdot (- 5)

simplificar (tan(x))/(sin^2(x))

s im pl i f y \frac{tan ( x )}{sin ^{2} ( x )}

simplificar (2-7m^6)2

s im pl i f y (2 - 7 m^{6}) 2

simplificar ((10!)/((10-5)!5!))(20/100)^5(80/100)^5

s im pl i f y (\frac{10 !}{( 10 - 5 ) ! 5 !}) (\frac{20}{100})^{5} (\frac{80}{100})^{5}

expandir (x-4)(x^2+6x-1)

e x p an d (x - 4) (x^{2} + 6 x - 1)