👉 Baixe o NerdPal agora! Nosso novo aplicativo de matemática no iOS e Android
  1. calculadoras
  2. Teorema Binomial

Calculadora de Teorema Binomial

Resolva seus problemas de matemática com nossa calculadora de Teorema Binomial passo a passo. Melhore suas habilidades matemáticas com nossa extensa lista de problemas difíceis. Encontre todas as nossas calculadoras aqui.

Go!
Modo simbolico
Modo texto
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

1

Aqui apresentamos um exemplo resolvido passo a passo de teorema binomial. Esta solução foi gerada automaticamente pela nossa calculadora inteligente:

$\left(x+3\right)^5$
2

Aplicamos a regra: $\left(a+b\right)^n$$=newton\left(\left(a+b\right)^n\right)$, onde $a=x$, $b=3$, $a+b=x+3$ e $n=5$

$\left(\begin{matrix}5\\0\end{matrix}\right)\cdot 3^{0}x^{5}+\left(\begin{matrix}5\\1\end{matrix}\right)\cdot 3^{1}x^{4}+\left(\begin{matrix}5\\2\end{matrix}\right)\cdot 3^{2}x^{3}+\left(\begin{matrix}5\\3\end{matrix}\right)\cdot 3^{3}x^{2}+\left(\begin{matrix}5\\4\end{matrix}\right)\cdot 3^{4}x^{1}+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 3^{5}x^{0}$
3

Aplicamos a regra: $a^b$$=a^b$, onde $a=3$, $b=0$ e $a^b=3^{0}$

$\left(\begin{matrix}5\\0\end{matrix}\right)x^{5}+\left(\begin{matrix}5\\1\end{matrix}\right)\cdot 3^{1}x^{4}+\left(\begin{matrix}5\\2\end{matrix}\right)\cdot 3^{2}x^{3}+\left(\begin{matrix}5\\3\end{matrix}\right)\cdot 3^{3}x^{2}+\left(\begin{matrix}5\\4\end{matrix}\right)\cdot 3^{4}x^{1}+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 3^{5}x^{0}$
4

Aplicamos a regra: $a^b$$=a^b$, onde $a=3$, $b=1$ e $a^b=3^{1}$

$\left(\begin{matrix}5\\0\end{matrix}\right)x^{5}+\left(\begin{matrix}5\\1\end{matrix}\right)\cdot 3x^{4}+\left(\begin{matrix}5\\2\end{matrix}\right)\cdot 3^{2}x^{3}+\left(\begin{matrix}5\\3\end{matrix}\right)\cdot 3^{3}x^{2}+\left(\begin{matrix}5\\4\end{matrix}\right)\cdot 3^{4}x^{1}+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 3^{5}x^{0}$
5

Aplicamos a regra: $a^b$$=a^b$, onde $a=3$, $b=2$ e $a^b=3^{2}$

$\left(\begin{matrix}5\\0\end{matrix}\right)x^{5}+\left(\begin{matrix}5\\1\end{matrix}\right)\cdot 3x^{4}+\left(\begin{matrix}5\\2\end{matrix}\right)\cdot 9x^{3}+\left(\begin{matrix}5\\3\end{matrix}\right)\cdot 3^{3}x^{2}+\left(\begin{matrix}5\\4\end{matrix}\right)\cdot 3^{4}x^{1}+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 3^{5}x^{0}$
6

Aplicamos a regra: $a^b$$=a^b$, onde $a=3$, $b=3$ e $a^b=3^{3}$

$\left(\begin{matrix}5\\0\end{matrix}\right)x^{5}+\left(\begin{matrix}5\\1\end{matrix}\right)\cdot 3x^{4}+\left(\begin{matrix}5\\2\end{matrix}\right)\cdot 9x^{3}+\left(\begin{matrix}5\\3\end{matrix}\right)\cdot 27x^{2}+\left(\begin{matrix}5\\4\end{matrix}\right)\cdot 3^{4}x^{1}+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 3^{5}x^{0}$
7

Aplicamos a regra: $a^b$$=a^b$, onde $a=3$, $b=4$ e $a^b=3^{4}$

$\left(\begin{matrix}5\\0\end{matrix}\right)x^{5}+\left(\begin{matrix}5\\1\end{matrix}\right)\cdot 3x^{4}+\left(\begin{matrix}5\\2\end{matrix}\right)\cdot 9x^{3}+\left(\begin{matrix}5\\3\end{matrix}\right)\cdot 27x^{2}+\left(\begin{matrix}5\\4\end{matrix}\right)\cdot 81x^{1}+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 3^{5}x^{0}$
8

Aplicamos a regra: $a^b$$=a^b$, onde $a=3$, $b=5$ e $a^b=3^{5}$

$\left(\begin{matrix}5\\0\end{matrix}\right)x^{5}+\left(\begin{matrix}5\\1\end{matrix}\right)\cdot 3x^{4}+\left(\begin{matrix}5\\2\end{matrix}\right)\cdot 9x^{3}+\left(\begin{matrix}5\\3\end{matrix}\right)\cdot 27x^{2}+\left(\begin{matrix}5\\4\end{matrix}\right)\cdot 81x^{1}+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243x^{0}$
9

Aplicamos a regra: $x^1$$=x$

$\left(\begin{matrix}5\\0\end{matrix}\right)x^{5}+\left(\begin{matrix}5\\1\end{matrix}\right)\cdot 3x^{4}+\left(\begin{matrix}5\\2\end{matrix}\right)\cdot 9x^{3}+\left(\begin{matrix}5\\3\end{matrix}\right)\cdot 27x^{2}+\left(\begin{matrix}5\\4\end{matrix}\right)\cdot 81x+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243x^{0}$
10

Aplicamos a regra: $x^0$$=1$

$\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 1\cdot 243$
11

Aplicamos a regra: $1x$$=x$, onde $x=\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243$

$\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243$
12

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=0$, $a,b=5,0$ e $bicoefa,b=\left(\begin{matrix}5\\0\end{matrix}\right)$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}$
13

Aplicamos a regra: $x!$$=x!$, onde $factx=0!$ e $x=0$

$\frac{5!}{\left(5+0\right)!}x^{5}$
14

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{\left(5+0\right)!}x^{5}$
15

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=0$, $a,b=5,0$ e $bicoefa,b=\left(\begin{matrix}5\\0\end{matrix}\right)$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}$
16

Aplicamos a regra: $x!$$=x!$, onde $factx=0!$ e $x=0$

$\frac{5!}{\left(5+0\right)!}x^{5}$
17

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{\left(5+0\right)!}x^{5}$
18

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=1$, $a,b=5,1$ e $bicoefa,b=\left(\begin{matrix}5\\1\end{matrix}\right)$

$\frac{5!}{\left(1!\right)\left(5-1\right)!}\cdot 3x^{4}$
19

Aplicamos a regra: $x!$$=x!$, onde $factx=1!$ e $x=1$

$\frac{5!}{\left(5-1\right)!}\cdot 3x^{4}$
20

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{\left(5-1\right)!}\cdot 3x^{4}$
21

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=0$, $a,b=5,0$ e $bicoefa,b=\left(\begin{matrix}5\\0\end{matrix}\right)$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}$
22

Aplicamos a regra: $x!$$=x!$, onde $factx=0!$ e $x=0$

$\frac{5!}{\left(5+0\right)!}x^{5}$
23

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{\left(5+0\right)!}x^{5}$
24

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=1$, $a,b=5,1$ e $bicoefa,b=\left(\begin{matrix}5\\1\end{matrix}\right)$

$\frac{5!}{\left(1!\right)\left(5-1\right)!}\cdot 3x^{4}$
25

Aplicamos a regra: $x!$$=x!$, onde $factx=1!$ e $x=1$

$\frac{5!}{\left(5-1\right)!}\cdot 3x^{4}$
26

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{\left(5-1\right)!}\cdot 3x^{4}$
27

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=2$, $a,b=5,2$ e $bicoefa,b=\left(\begin{matrix}5\\2\end{matrix}\right)$

$\frac{5!}{\left(2!\right)\left(5-2\right)!}\cdot 9x^{3}$
28

Aplicamos a regra: $x!$$=x!$, onde $factx=2!$ e $x=2$

$\frac{5!}{2\left(5-2\right)!}\cdot 9x^{3}$
29

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{2\left(5-2\right)!}\cdot 9x^{3}$
30

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=0$, $a,b=5,0$ e $bicoefa,b=\left(\begin{matrix}5\\0\end{matrix}\right)$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}$
31

Aplicamos a regra: $x!$$=x!$, onde $factx=0!$ e $x=0$

$\frac{5!}{\left(5+0\right)!}x^{5}$
32

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{\left(5+0\right)!}x^{5}$
33

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=1$, $a,b=5,1$ e $bicoefa,b=\left(\begin{matrix}5\\1\end{matrix}\right)$

$\frac{5!}{\left(1!\right)\left(5-1\right)!}\cdot 3x^{4}$
34

Aplicamos a regra: $x!$$=x!$, onde $factx=1!$ e $x=1$

$\frac{5!}{\left(5-1\right)!}\cdot 3x^{4}$
35

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{\left(5-1\right)!}\cdot 3x^{4}$
36

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=2$, $a,b=5,2$ e $bicoefa,b=\left(\begin{matrix}5\\2\end{matrix}\right)$

$\frac{5!}{\left(2!\right)\left(5-2\right)!}\cdot 9x^{3}$
37

Aplicamos a regra: $x!$$=x!$, onde $factx=2!$ e $x=2$

$\frac{5!}{2\left(5-2\right)!}\cdot 9x^{3}$
38

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{2\left(5-2\right)!}\cdot 9x^{3}$
39

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=3$, $a,b=5,3$ e $bicoefa,b=\left(\begin{matrix}5\\3\end{matrix}\right)$

$\frac{5!}{\left(3!\right)\left(5-3\right)!}\cdot 27x^{2}$
40

Aplicamos a regra: $x!$$=x!$, onde $factx=3!$ e $x=3$

$\frac{5!}{6\left(5-3\right)!}\cdot 27x^{2}$
41

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{6\left(5-3\right)!}\cdot 27x^{2}$
42

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=0$, $a,b=5,0$ e $bicoefa,b=\left(\begin{matrix}5\\0\end{matrix}\right)$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}$
43

Aplicamos a regra: $x!$$=x!$, onde $factx=0!$ e $x=0$

$\frac{5!}{\left(5+0\right)!}x^{5}$
44

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{\left(5+0\right)!}x^{5}$
45

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=1$, $a,b=5,1$ e $bicoefa,b=\left(\begin{matrix}5\\1\end{matrix}\right)$

$\frac{5!}{\left(1!\right)\left(5-1\right)!}\cdot 3x^{4}$
46

Aplicamos a regra: $x!$$=x!$, onde $factx=1!$ e $x=1$

$\frac{5!}{\left(5-1\right)!}\cdot 3x^{4}$
47

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{\left(5-1\right)!}\cdot 3x^{4}$
48

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=2$, $a,b=5,2$ e $bicoefa,b=\left(\begin{matrix}5\\2\end{matrix}\right)$

$\frac{5!}{\left(2!\right)\left(5-2\right)!}\cdot 9x^{3}$
49

Aplicamos a regra: $x!$$=x!$, onde $factx=2!$ e $x=2$

$\frac{5!}{2\left(5-2\right)!}\cdot 9x^{3}$
50

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{2\left(5-2\right)!}\cdot 9x^{3}$
51

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=3$, $a,b=5,3$ e $bicoefa,b=\left(\begin{matrix}5\\3\end{matrix}\right)$

$\frac{5!}{\left(3!\right)\left(5-3\right)!}\cdot 27x^{2}$
52

Aplicamos a regra: $x!$$=x!$, onde $factx=3!$ e $x=3$

$\frac{5!}{6\left(5-3\right)!}\cdot 27x^{2}$
53

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{6\left(5-3\right)!}\cdot 27x^{2}$
54

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=4$, $a,b=5,4$ e $bicoefa,b=\left(\begin{matrix}5\\4\end{matrix}\right)$

$\frac{5!}{\left(4!\right)\left(5-4\right)!}\cdot 81x$
55

Aplicamos a regra: $x!$$=x!$, onde $factx=4!$ e $x=4$

$\frac{5!}{24\left(5-4\right)!}\cdot 81x$
56

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{24\left(5-4\right)!}\cdot 81x$
57

Aplicamos a regra: $a+b$$=a+b$, onde $a=5$, $b=-1$ e $a+b=5-1$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(5-2\right)!}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(5-3\right)!}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(5-4\right)!}x+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243$
58

Aplicamos a regra: $a+b$$=a+b$, onde $a=5$, $b=-2$ e $a+b=5-2$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(5-3\right)!}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(5-4\right)!}x+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243$
59

Aplicamos a regra: $a+b$$=a+b$, onde $a=5$, $b=-3$ e $a+b=5-3$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(5-4\right)!}x+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243$
60

Aplicamos a regra: $a+b$$=a+b$, onde $a=5$, $b=-4$ e $a+b=5-4$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243$
61

Aplicamos a regra: $a+b$$=a+b$, onde $a=5$, $b=0$ e $a+b=5+0$

$\frac{5!}{\left(0!\right)\left(5!\right)}x^{5}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243$
62

Aplicamos a regra: $\frac{a}{a}$$=1$, onde $a/a=\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}$

$\frac{1}{0!}x^{5}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243$
63

Aplicamos a regra: $a\frac{1}{x}$$=\frac{a}{x}$

$\frac{x^{5}}{0!}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243$
64

Aplicamos a regra: $a\frac{b}{c}$$=\frac{ba}{c}$, onde $a=x^{4}$, $b=3\left(5!\right)$ e $c=\left(1!\right)\left(4!\right)$

$\frac{x^{5}}{0!}+\frac{3\left(5!\right)\left(x^{4}\right)}{\left(1!\right)\left(4!\right)}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243$
65

Aplicamos a regra: $a\frac{b}{c}$$=\frac{ba}{c}$, onde $a=x^{3}$, $b=9\left(5!\right)$ e $c=\left(2!\right)\left(3!\right)$

$\frac{x^{5}}{0!}+\frac{3\left(5!\right)\left(x^{4}\right)}{\left(1!\right)\left(4!\right)}+\frac{9\left(5!\right)\left(x^{3}\right)}{\left(2!\right)\left(3!\right)}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243$
66

Aplicamos a regra: $a\frac{b}{c}$$=\frac{ba}{c}$, onde $a=x^{2}$, $b=27\left(5!\right)$ e $c=\left(3!\right)\left(2!\right)$

$\frac{x^{5}}{0!}+\frac{3\left(5!\right)\left(x^{4}\right)}{\left(1!\right)\left(4!\right)}+\frac{9\left(5!\right)\left(x^{3}\right)}{\left(2!\right)\left(3!\right)}+\frac{27\left(5!\right)\left(x^{2}\right)}{\left(3!\right)\left(2!\right)}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243$
67

Aplicamos a regra: $a\frac{b}{c}$$=\frac{ba}{c}$, onde $a=x$, $b=81\left(5!\right)$ e $c=\left(4!\right)\left(1!\right)$

$\frac{x^{5}}{0!}+\frac{3\left(5!\right)\left(x^{4}\right)}{\left(1!\right)\left(4!\right)}+\frac{9\left(5!\right)\left(x^{3}\right)}{\left(2!\right)\left(3!\right)}+\frac{27\left(5!\right)\left(x^{2}\right)}{\left(3!\right)\left(2!\right)}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243$
68

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=0$, $a,b=5,0$ e $bicoefa,b=\left(\begin{matrix}5\\0\end{matrix}\right)$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}$
69

Aplicamos a regra: $x!$$=x!$, onde $factx=0!$ e $x=0$

$\frac{5!}{\left(5+0\right)!}x^{5}$
70

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{\left(5+0\right)!}x^{5}$
71

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=1$, $a,b=5,1$ e $bicoefa,b=\left(\begin{matrix}5\\1\end{matrix}\right)$

$\frac{5!}{\left(1!\right)\left(5-1\right)!}\cdot 3x^{4}$
72

Aplicamos a regra: $x!$$=x!$, onde $factx=1!$ e $x=1$

$\frac{5!}{\left(5-1\right)!}\cdot 3x^{4}$
73

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{\left(5-1\right)!}\cdot 3x^{4}$
74

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=2$, $a,b=5,2$ e $bicoefa,b=\left(\begin{matrix}5\\2\end{matrix}\right)$

$\frac{5!}{\left(2!\right)\left(5-2\right)!}\cdot 9x^{3}$
75

Aplicamos a regra: $x!$$=x!$, onde $factx=2!$ e $x=2$

$\frac{5!}{2\left(5-2\right)!}\cdot 9x^{3}$
76

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{2\left(5-2\right)!}\cdot 9x^{3}$
77

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=3$, $a,b=5,3$ e $bicoefa,b=\left(\begin{matrix}5\\3\end{matrix}\right)$

$\frac{5!}{\left(3!\right)\left(5-3\right)!}\cdot 27x^{2}$
78

Aplicamos a regra: $x!$$=x!$, onde $factx=3!$ e $x=3$

$\frac{5!}{6\left(5-3\right)!}\cdot 27x^{2}$
79

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{6\left(5-3\right)!}\cdot 27x^{2}$
80

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=4$, $a,b=5,4$ e $bicoefa,b=\left(\begin{matrix}5\\4\end{matrix}\right)$

$\frac{5!}{\left(4!\right)\left(5-4\right)!}\cdot 81x$
81

Aplicamos a regra: $x!$$=x!$, onde $factx=4!$ e $x=4$

$\frac{5!}{24\left(5-4\right)!}\cdot 81x$
82

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{120}{24\left(5-4\right)!}\cdot 81x$
83

Aplicamos a regra: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, onde $a=5$, $b=5$, $a,b=5,5$ e $bicoefa,b=\left(\begin{matrix}5\\5\end{matrix}\right)$

$\left(\frac{5!}{\left(5!\right)\left(5-5\right)!}\right)\cdot 243$
84

Aplicamos a regra: $\frac{a}{a}$$=1$, onde $a/a=\frac{1}{\left(5-5\right)!}$

$\left(\frac{1}{\left(5-5\right)!}\right)\cdot 243$
85

Aplicamos a regra: $a+b$$=a+b$, onde $a=5$, $b=-5$ e $a+b=5-5$

$\frac{x^{5}}{0!}+\frac{3\left(5!\right)\left(x^{4}\right)}{\left(1!\right)\left(4!\right)}+\frac{9\left(5!\right)\left(x^{3}\right)}{\left(2!\right)\left(3!\right)}+\frac{27\left(5!\right)\left(x^{2}\right)}{\left(3!\right)\left(2!\right)}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243\left(5!\right)}{\left(5!\right)\left(0!\right)}$
86

Aplicamos a regra: $\frac{a}{a}$$=1$, onde $a/a=\frac{243}{0!}$

$\frac{x^{5}}{0!}+\frac{3\left(5!\right)\left(x^{4}\right)}{\left(1!\right)\left(4!\right)}+\frac{9\left(5!\right)\left(x^{3}\right)}{\left(2!\right)\left(3!\right)}+\frac{27\left(5!\right)\left(x^{2}\right)}{\left(3!\right)\left(2!\right)}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
87

Aplicamos a regra: $x!$$=x!$, onde $factx=0!$ e $x=0$

$\frac{x^{5}}{1}+\frac{3\left(5!\right)\left(x^{4}\right)}{\left(1!\right)\left(4!\right)}+\frac{9\left(5!\right)\left(x^{3}\right)}{\left(2!\right)\left(3!\right)}+\frac{27\left(5!\right)\left(x^{2}\right)}{\left(3!\right)\left(2!\right)}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
88

Aplicamos a regra: $x!$$=x!$, onde $factx=1!$ e $x=1$

$\frac{x^{5}}{1}+\frac{3\left(5!\right)\left(x^{4}\right)}{4!}+\frac{9\left(5!\right)\left(x^{3}\right)}{\left(2!\right)\left(3!\right)}+\frac{27\left(5!\right)\left(x^{2}\right)}{\left(3!\right)\left(2!\right)}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
89

Aplicamos a regra: $x!$$=x!$, onde $factx=4!$ e $x=4$

$\frac{x^{5}}{1}+\frac{3\left(5!\right)\left(x^{4}\right)}{24}+\frac{9\left(5!\right)\left(x^{3}\right)}{\left(2!\right)\left(3!\right)}+\frac{27\left(5!\right)\left(x^{2}\right)}{\left(3!\right)\left(2!\right)}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
90

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$\frac{x^{5}}{1}+\frac{3\cdot 120x^{4}}{24}+\frac{9\left(5!\right)\left(x^{3}\right)}{\left(2!\right)\left(3!\right)}+\frac{27\left(5!\right)\left(x^{2}\right)}{\left(3!\right)\left(2!\right)}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
91

Aplicamos a regra: $x!$$=x!$, onde $factx=2!$ e $x=2$

$\frac{x^{5}}{1}+\frac{3\cdot 120x^{4}}{24}+\frac{9\left(5!\right)\left(x^{3}\right)}{2\left(3!\right)}+\frac{27\left(5!\right)\left(x^{2}\right)}{\left(3!\right)\left(2!\right)}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
92

Aplicamos a regra: $ab$$=ab$, onde $ab=3\cdot 120x^{4}$, $a=3$ e $b=120$

$\frac{x^{5}}{1}+\frac{360x^{4}}{24}+\frac{9\left(5!\right)\left(x^{3}\right)}{2\left(3!\right)}+\frac{27\left(5!\right)\left(x^{2}\right)}{\left(3!\right)\left(2!\right)}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
93

Aplicamos a regra: $\frac{x}{1}$$=x$, onde $x=x^{5}$

$x^{5}+\frac{360x^{4}}{24}+\frac{9\left(5!\right)\left(x^{3}\right)}{2\left(3!\right)}+\frac{27\left(5!\right)\left(x^{2}\right)}{\left(3!\right)\left(2!\right)}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
94

Aplicamos a regra: $\frac{ab}{c}$$=\frac{a}{c}b$, onde $ab=360x^{4}$, $a=360$, $b=x^{4}$, $c=24$ e $ab/c=\frac{360x^{4}}{24}$

$x^{5}+15x^{4}+\frac{9\left(5!\right)\left(x^{3}\right)}{2\left(3!\right)}+\frac{27\left(5!\right)\left(x^{2}\right)}{\left(3!\right)\left(2!\right)}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
95

Aplicamos a regra: $x!$$=x!$, onde $factx=3!$ e $x=3$

$x^{5}+15x^{4}+\frac{9\left(5!\right)\left(x^{3}\right)}{2\cdot 6}+\frac{27\left(5!\right)\left(x^{2}\right)}{\left(3!\right)\left(2!\right)}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
96

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$x^{5}+15x^{4}+\frac{9\cdot 120x^{3}}{2\cdot 6}+\frac{27\left(5!\right)\left(x^{2}\right)}{\left(3!\right)\left(2!\right)}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
97

Aplicamos a regra: $x!$$=x!$, onde $factx=3!$ e $x=3$

$x^{5}+15x^{4}+\frac{9\cdot 120x^{3}}{2\cdot 6}+\frac{27\left(5!\right)\left(x^{2}\right)}{6\left(2!\right)}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
98

Aplicamos a regra: $x!$$=x!$, onde $factx=2!$ e $x=2$

$x^{5}+15x^{4}+\frac{9\cdot 120x^{3}}{2\cdot 6}+\frac{27\left(5!\right)\left(x^{2}\right)}{6\cdot 2}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
99

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$x^{5}+15x^{4}+\frac{9\cdot 120x^{3}}{2\cdot 6}+\frac{27\cdot 120x^{2}}{6\cdot 2}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
100

Aplicamos a regra: $ab$$=ab$, onde $ab=2\cdot 6$, $a=2$ e $b=6$

$x^{5}+15x^{4}+\frac{9\cdot 120x^{3}}{12}+\frac{27\cdot 120x^{2}}{6\cdot 2}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
101

Aplicamos a regra: $ab$$=ab$, onde $ab=9\cdot 120x^{3}$, $a=9$ e $b=120$

$x^{5}+15x^{4}+\frac{1080x^{3}}{12}+\frac{27\cdot 120x^{2}}{6\cdot 2}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
102

Aplicamos a regra: $ab$$=ab$, onde $ab=6\cdot 2$, $a=6$ e $b=2$

$x^{5}+15x^{4}+\frac{1080x^{3}}{12}+\frac{27\cdot 120x^{2}}{12}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
103

Aplicamos a regra: $ab$$=ab$, onde $ab=27\cdot 120x^{2}$, $a=27$ e $b=120$

$x^{5}+15x^{4}+\frac{1080x^{3}}{12}+\frac{3240x^{2}}{12}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
104

Aplicamos a regra: $\frac{ab}{c}$$=\frac{a}{c}b$, onde $ab=1080x^{3}$, $a=1080$, $b=x^{3}$, $c=12$ e $ab/c=\frac{1080x^{3}}{12}$

$x^{5}+15x^{4}+90x^{3}+\frac{3240x^{2}}{12}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
105

Aplicamos a regra: $\frac{ab}{c}$$=\frac{a}{c}b$, onde $ab=3240x^{2}$, $a=3240$, $b=x^{2}$, $c=12$ e $ab/c=\frac{3240x^{2}}{12}$

$x^{5}+15x^{4}+90x^{3}+270x^{2}+\frac{81\left(5!\right)x}{\left(4!\right)\left(1!\right)}+\frac{243}{0!}$
106

Aplicamos a regra: $x!$$=x!$, onde $factx=4!$ e $x=4$

$x^{5}+15x^{4}+90x^{3}+270x^{2}+\frac{81\left(5!\right)x}{24\left(1!\right)}+\frac{243}{0!}$
107

Aplicamos a regra: $x!$$=x!$, onde $factx=1!$ e $x=1$

$x^{5}+15x^{4}+90x^{3}+270x^{2}+\frac{81\left(5!\right)x}{24}+\frac{243}{0!}$
108

Aplicamos a regra: $x!$$=x!$, onde $factx=5!$ e $x=5$

$x^{5}+15x^{4}+90x^{3}+270x^{2}+\frac{81\cdot 120x}{24}+\frac{243}{0!}$
109

Aplicamos a regra: $x!$$=x!$, onde $factx=0!$ e $x=0$

$x^{5}+15x^{4}+90x^{3}+270x^{2}+\frac{81\cdot 120x}{24}+\frac{243}{1}$
110

Aplicamos a regra: $ab$$=ab$, onde $ab=81\cdot 120x$, $a=81$ e $b=120$

$x^{5}+15x^{4}+90x^{3}+270x^{2}+\frac{9720x}{24}+\frac{243}{1}$
111

Aplicamos a regra: $\frac{a}{b}$$=\frac{a}{b}$, onde $a=243$, $b=1$ e $a/b=\frac{243}{1}$

$x^{5}+15x^{4}+90x^{3}+270x^{2}+\frac{9720x}{24}+243$
112

Aplicamos a regra: $\frac{ab}{c}$$=\frac{a}{c}b$, onde $ab=9720x$, $a=9720$, $b=x$, $c=24$ e $ab/c=\frac{9720x}{24}$

$x^{5}+15x^{4}+90x^{3}+270x^{2}+405x+243$

Resposta final para o problema

$x^{5}+15x^{4}+90x^{3}+270x^{2}+405x+243$

Você tem dificuldades com matemática?

Tenha acesso a milhares de soluções de exercícios passo a passo e elas crescem a cada dia!