es

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Álgebra >

desarrollar (2x+1)^8

Solución

desarrollar

(2 x + 1)^{8}

Solución

256 x^{8} + 1024 x^{7} + 1792 x^{6} + 1792 x^{5} + 1120 x^{4} + 448 x^{3} + 112 x^{2} + 16 x + 1

Pasos de solución

(2 x + 1)^{8}

Aplicar el teorema del binomio:

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

a = 2 x, b = 1

= i = 0 \sum 8 (i 8) (2 x)^{(8 - i)} \cdot 1^{i}

Expandir sumatorio

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

Simplificar

\frac{8 !}{0 ! ( 8 - 0 ) !} (2 x)^{8} \cdot 1^{0} : 256 x^{8}

Simplificar

\frac{8 !}{1 ! ( 8 - 1 ) !} (2 x)^{7} \cdot 1^{1} : 1024 x^{7}

Simplificar

\frac{8 !}{2 ! ( 8 - 2 ) !} (2 x)^{6} \cdot 1^{2} : 1792 x^{6}

Simplificar

\frac{8 !}{3 ! ( 8 - 3 ) !} (2 x)^{5} \cdot 1^{3} : 1792 x^{5}

Simplificar

\frac{8 !}{4 ! ( 8 - 4 ) !} (2 x)^{4} \cdot 1^{4} : 1120 x^{4}

Simplificar

\frac{8 !}{5 ! ( 8 - 5 ) !} (2 x)^{3} \cdot 1^{5} : 448 x^{3}

Simplificar

\frac{8 !}{6 ! ( 8 - 6 ) !} (2 x)^{2} \cdot 1^{6} : 112 x^{2}

Simplificar

\frac{8 !}{7 ! ( 8 - 7 ) !} (2 x)^{1} \cdot 1^{7} : 16 x

Simplificar

\frac{8 !}{8 ! ( 8 - 8 ) !} (2 x)^{0} \cdot 1^{8} : 1

= 256 x^{8} + 1024 x^{7} + 1792 x^{6} + 1792 x^{5} + 1120 x^{4} + 448 x^{3} + 112 x^{2} + 16 x + 1

Ejemplos populares

\frac{15}{4} \div \frac{1}{5}

factor x^2*+x^3

f a c t or x^{2} \cdot + x^{3}

simplificar (j-7)/(j-6)-(2j+5)/(j^2+8j+12)

s im pl i f y \frac{j - 7}{j - 6} - \frac{2 j + 5}{j ^{2} + 8 j + 12}

simplificar 16× 16× 16

s im pl i f y 16 \times 16 \times 16

simplificar sqrt(x^4y^2)+2x^2+y^4

s im pl i f y x^{4} y^{2} + 2 x^{2} + y^{4}