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Calculatrice Théorème binomial

Résolvez vos problèmes de mathématiques avec notre calculatrice Théorème binomial étape par étape. Améliorez vos compétences en mathématiques grâce à notre longue liste de problèmes difficiles. Retrouvez tous nos calculateurs ici.

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1

Qui vi mostriamo un esempio di soluzione passo-passo di teorema di binomio. Questa soluzione è stata generata automaticamente dalla nostra calcolatrice intelligente:

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

Applicare la formula: $\left(a+b\right)^n$$=newton\left(\left(a+b\right)^n\right)$, dove $a=x$, $b=3$, $a+b=x+3$ 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

Applicare la formula: $a^b$$=a^b$, dove $a=3$, $b=0$ e $a^b=3^{0}$

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

Applicare la formula: $a^b$$=a^b$, dove $a=3$, $b=1$ e $a^b=3^{1}$

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

Applicare la formula: $a^b$$=a^b$, dove $a=3$, $b=2$ e $a^b=3^{2}$

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

Applicare la formula: $a^b$$=a^b$, dove $a=3$, $b=3$ e $a^b=3^{3}$

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

Applicare la formula: $a^b$$=a^b$, dove $a=3$, $b=4$ e $a^b=3^{4}$

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

Applicare la formula: $a^b$$=a^b$, dove $a=3$, $b=5$ e $a^b=3^{5}$

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

Applicare la formula: $x^1$$=x$

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

Applicare la formula: $1x$$=x$, dove $x=\left(\begin{matrix}5\\0\end{matrix}\right)x^{5}$

$\left(\begin{matrix}5\\0\end{matrix}\right)x^{5}+3\left(\begin{matrix}5\\1\end{matrix}\right)x^{4}+9\left(\begin{matrix}5\\2\end{matrix}\right)x^{3}+27\left(\begin{matrix}5\\3\end{matrix}\right)x^{2}+81\left(\begin{matrix}5\\4\end{matrix}\right)x+243\left(\begin{matrix}5\\5\end{matrix}\right)x^{0}$
11

Applicare la formula: $x^0$$=1$

$\left(\begin{matrix}5\\0\end{matrix}\right)x^{5}+3\left(\begin{matrix}5\\1\end{matrix}\right)x^{4}+9\left(\begin{matrix}5\\2\end{matrix}\right)x^{3}+27\left(\begin{matrix}5\\3\end{matrix}\right)x^{2}+81\left(\begin{matrix}5\\4\end{matrix}\right)x+243\left(\begin{matrix}5\\5\end{matrix}\right)$
12

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=0$, $a,b=5,0$ e $bicoefa,b=\left(\begin{matrix}5\\0\end{matrix}\right)$

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

Applicare la formula: $x!$$=x!$, dove $factx=0!$ e $x=0$

$\frac{5!}{1\cdot 1}x^{5}$
14

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$\frac{120}{1\cdot 1}x^{5}$
15

Applicare la formula: $1x$$=x$, dove $x=1$

$120x^{5}$
16

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=0$, $a,b=5,0$ e $bicoefa,b=\left(\begin{matrix}5\\0\end{matrix}\right)$

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

Applicare la formula: $x!$$=x!$, dove $factx=0!$ e $x=0$

$\frac{5!}{1\cdot 1}x^{5}$
18

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$\frac{120}{1\cdot 1}x^{5}$
19

Applicare la formula: $1x$$=x$, dove $x=1$

$120x^{5}$
20

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=1$, $a,b=5,1$ e $bicoefa,b=\left(\begin{matrix}5\\1\end{matrix}\right)$

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

Applicare la formula: $x!$$=x!$, dove $factx=1!$ e $x=1$

$3\frac{5!}{1\cdot 1}x^{4}$
22

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$3\frac{120}{1\cdot 1}x^{4}$
23

Applicare la formula: $1x$$=x$, dove $x=1$

$120\cdot 3x^{4}$
24

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=0$, $a,b=5,0$ e $bicoefa,b=\left(\begin{matrix}5\\0\end{matrix}\right)$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}$
25

Applicare la formula: $x!$$=x!$, dove $factx=0!$ e $x=0$

$\frac{5!}{1\cdot 1}x^{5}$
26

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$\frac{120}{1\cdot 1}x^{5}$
27

Applicare la formula: $1x$$=x$, dove $x=1$

$120x^{5}$
28

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=1$, $a,b=5,1$ e $bicoefa,b=\left(\begin{matrix}5\\1\end{matrix}\right)$

$3\frac{5!}{\left(1!\right)\left(5-1\right)!}x^{4}$
29

Applicare la formula: $x!$$=x!$, dove $factx=1!$ e $x=1$

$3\frac{5!}{1\cdot 1}x^{4}$
30

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$3\frac{120}{1\cdot 1}x^{4}$
31

Applicare la formula: $1x$$=x$, dove $x=1$

$120\cdot 3x^{4}$
32

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=2$, $a,b=5,2$ e $bicoefa,b=\left(\begin{matrix}5\\2\end{matrix}\right)$

$9\frac{5!}{\left(2!\right)\left(5-2\right)!}x^{3}$
33

Applicare la formula: $x!$$=x!$, dove $factx=2!$ e $x=2$

$9\frac{5!}{2\cdot 1}x^{3}$
34

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$9\frac{120}{2\cdot 1}x^{3}$
35

Applicare la formula: $1x$$=x$, dove $x=2$

$9\frac{120}{2}x^{3}$
36

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=0$, $a,b=5,0$ e $bicoefa,b=\left(\begin{matrix}5\\0\end{matrix}\right)$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}$
37

Applicare la formula: $x!$$=x!$, dove $factx=0!$ e $x=0$

$\frac{5!}{1\cdot 1}x^{5}$
38

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$\frac{120}{1\cdot 1}x^{5}$
39

Applicare la formula: $1x$$=x$, dove $x=1$

$120x^{5}$
40

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=1$, $a,b=5,1$ e $bicoefa,b=\left(\begin{matrix}5\\1\end{matrix}\right)$

$3\frac{5!}{\left(1!\right)\left(5-1\right)!}x^{4}$
41

Applicare la formula: $x!$$=x!$, dove $factx=1!$ e $x=1$

$3\frac{5!}{1\cdot 1}x^{4}$
42

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$3\frac{120}{1\cdot 1}x^{4}$
43

Applicare la formula: $1x$$=x$, dove $x=1$

$120\cdot 3x^{4}$
44

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=2$, $a,b=5,2$ e $bicoefa,b=\left(\begin{matrix}5\\2\end{matrix}\right)$

$9\frac{5!}{\left(2!\right)\left(5-2\right)!}x^{3}$
45

Applicare la formula: $x!$$=x!$, dove $factx=2!$ e $x=2$

$9\frac{5!}{2\cdot 1}x^{3}$
46

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$9\frac{120}{2\cdot 1}x^{3}$
47

Applicare la formula: $1x$$=x$, dove $x=2$

$9\frac{120}{2}x^{3}$
48

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=3$, $a,b=5,3$ e $bicoefa,b=\left(\begin{matrix}5\\3\end{matrix}\right)$

$27\frac{5!}{\left(3!\right)\left(5-3\right)!}x^{2}$
49

Applicare la formula: $x!$$=x!$, dove $factx=3!$ e $x=3$

$27\frac{5!}{6\cdot 1}x^{2}$
50

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$27\frac{120}{6\cdot 1}x^{2}$
51

Applicare la formula: $1x$$=x$, dove $x=6$

$27\frac{120}{6}x^{2}$
52

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=0$, $a,b=5,0$ e $bicoefa,b=\left(\begin{matrix}5\\0\end{matrix}\right)$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}$
53

Applicare la formula: $x!$$=x!$, dove $factx=0!$ e $x=0$

$\frac{5!}{1\cdot 1}x^{5}$
54

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$\frac{120}{1\cdot 1}x^{5}$
55

Applicare la formula: $1x$$=x$, dove $x=1$

$120x^{5}$
56

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=1$, $a,b=5,1$ e $bicoefa,b=\left(\begin{matrix}5\\1\end{matrix}\right)$

$3\frac{5!}{\left(1!\right)\left(5-1\right)!}x^{4}$
57

Applicare la formula: $x!$$=x!$, dove $factx=1!$ e $x=1$

$3\frac{5!}{1\cdot 1}x^{4}$
58

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$3\frac{120}{1\cdot 1}x^{4}$
59

Applicare la formula: $1x$$=x$, dove $x=1$

$120\cdot 3x^{4}$
60

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=2$, $a,b=5,2$ e $bicoefa,b=\left(\begin{matrix}5\\2\end{matrix}\right)$

$9\frac{5!}{\left(2!\right)\left(5-2\right)!}x^{3}$
61

Applicare la formula: $x!$$=x!$, dove $factx=2!$ e $x=2$

$9\frac{5!}{2\cdot 1}x^{3}$
62

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$9\frac{120}{2\cdot 1}x^{3}$
63

Applicare la formula: $1x$$=x$, dove $x=2$

$9\frac{120}{2}x^{3}$
64

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=3$, $a,b=5,3$ e $bicoefa,b=\left(\begin{matrix}5\\3\end{matrix}\right)$

$27\frac{5!}{\left(3!\right)\left(5-3\right)!}x^{2}$
65

Applicare la formula: $x!$$=x!$, dove $factx=3!$ e $x=3$

$27\frac{5!}{6\cdot 1}x^{2}$
66

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$27\frac{120}{6\cdot 1}x^{2}$
67

Applicare la formula: $1x$$=x$, dove $x=6$

$27\frac{120}{6}x^{2}$
68

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=4$, $a,b=5,4$ e $bicoefa,b=\left(\begin{matrix}5\\4\end{matrix}\right)$

$81\frac{5!}{\left(4!\right)\left(5-4\right)!}x$
69

Applicare la formula: $x!$$=x!$, dove $factx=4!$ e $x=4$

$81\frac{5!}{24\cdot 1}x$
70

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$81\frac{120}{24\cdot 1}x$
71

Applicare la formula: $1x$$=x$, dove $x=24$

$81\frac{120}{24}x$
72

Applicare la formula: $a+b$$=a+b$, dove $a=5$, $b=-1$ e $a+b=5-1$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(5-2\right)!}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(5-3\right)!}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(5-4\right)!}x+243\left(\begin{matrix}5\\5\end{matrix}\right)$
73

Applicare la formula: $a+b$$=a+b$, dove $a=5$, $b=-2$ e $a+b=5-2$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(5-3\right)!}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(5-4\right)!}x+243\left(\begin{matrix}5\\5\end{matrix}\right)$
74

Applicare la formula: $a+b$$=a+b$, dove $a=5$, $b=-3$ e $a+b=5-3$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(5-4\right)!}x+243\left(\begin{matrix}5\\5\end{matrix}\right)$
75

Applicare la formula: $a+b$$=a+b$, dove $a=5$, $b=-4$ e $a+b=5-4$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+243\left(\begin{matrix}5\\5\end{matrix}\right)$
76

Applicare la formula: $a+b$$=a+b$, dove $a=5$, $b=0$ e $a+b=5+0$

$\frac{5!}{\left(0!\right)\left(5!\right)}x^{5}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+243\left(\begin{matrix}5\\5\end{matrix}\right)$
77

Applicare la formula: $\frac{a}{a}$$=1$, dove $a=5!$ e $a/a=\frac{5!}{\left(0!\right)\left(5!\right)}$

$\frac{1}{0!}x^{5}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+243\left(\begin{matrix}5\\5\end{matrix}\right)$
78

Applicare la formula: $a\frac{b}{x}$$=\frac{ab}{x}$

$\frac{1x^{5}}{0!}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+243\left(\begin{matrix}5\\5\end{matrix}\right)$
79

Applicare la formula: $1x$$=x$, dove $x=x^{5}$

$\frac{x^{5}}{0!}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+243\left(\begin{matrix}5\\5\end{matrix}\right)$
80

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=0$, $a,b=5,0$ e $bicoefa,b=\left(\begin{matrix}5\\0\end{matrix}\right)$

$\frac{5!}{\left(0!\right)\left(5+0\right)!}x^{5}$
81

Applicare la formula: $x!$$=x!$, dove $factx=0!$ e $x=0$

$\frac{5!}{1\cdot 1}x^{5}$
82

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$\frac{120}{1\cdot 1}x^{5}$
83

Applicare la formula: $1x$$=x$, dove $x=1$

$120x^{5}$
84

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=1$, $a,b=5,1$ e $bicoefa,b=\left(\begin{matrix}5\\1\end{matrix}\right)$

$3\frac{5!}{\left(1!\right)\left(5-1\right)!}x^{4}$
85

Applicare la formula: $x!$$=x!$, dove $factx=1!$ e $x=1$

$3\frac{5!}{1\cdot 1}x^{4}$
86

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$3\frac{120}{1\cdot 1}x^{4}$
87

Applicare la formula: $1x$$=x$, dove $x=1$

$120\cdot 3x^{4}$
88

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=2$, $a,b=5,2$ e $bicoefa,b=\left(\begin{matrix}5\\2\end{matrix}\right)$

$9\frac{5!}{\left(2!\right)\left(5-2\right)!}x^{3}$
89

Applicare la formula: $x!$$=x!$, dove $factx=2!$ e $x=2$

$9\frac{5!}{2\cdot 1}x^{3}$
90

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$9\frac{120}{2\cdot 1}x^{3}$
91

Applicare la formula: $1x$$=x$, dove $x=2$

$9\frac{120}{2}x^{3}$
92

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=3$, $a,b=5,3$ e $bicoefa,b=\left(\begin{matrix}5\\3\end{matrix}\right)$

$27\frac{5!}{\left(3!\right)\left(5-3\right)!}x^{2}$
93

Applicare la formula: $x!$$=x!$, dove $factx=3!$ e $x=3$

$27\frac{5!}{6\cdot 1}x^{2}$
94

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$27\frac{120}{6\cdot 1}x^{2}$
95

Applicare la formula: $1x$$=x$, dove $x=6$

$27\frac{120}{6}x^{2}$
96

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=4$, $a,b=5,4$ e $bicoefa,b=\left(\begin{matrix}5\\4\end{matrix}\right)$

$81\frac{5!}{\left(4!\right)\left(5-4\right)!}x$
97

Applicare la formula: $x!$$=x!$, dove $factx=4!$ e $x=4$

$81\frac{5!}{24\cdot 1}x$
98

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$81\frac{120}{24\cdot 1}x$
99

Applicare la formula: $1x$$=x$, dove $x=24$

$81\frac{120}{24}x$
100

Applicare la formula: $\left(\begin{matrix}a\\b\end{matrix}\right)$$=\frac{a!}{\left(b!\right)\left(a-b\right)!}$, dove $a=5$, $b=5$, $a,b=5,5$ e $bicoefa,b=\left(\begin{matrix}5\\5\end{matrix}\right)$

$243\left(\frac{5!}{\left(5!\right)\left(5-5\right)!}\right)$
101

Applicare la formula: $\frac{a}{a}$$=1$, dove $a=5!$ e $a/a=\frac{5!}{\left(5!\right)\left(5-5\right)!}$

$243\left(\frac{1}{\left(5-5\right)!}\right)$
102

Applicare la formula: $a+b$$=a+b$, dove $a=5$, $b=-5$ e $a+b=5-5$

$\frac{x^{5}}{0!}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\frac{243\left(5!\right)}{\left(5!\right)\left(0!\right)}$
103

Applicare la formula: $\frac{a}{a}$$=1$, dove $a=5!$ e $a/a=\frac{243\left(5!\right)}{\left(5!\right)\left(0!\right)}$

$\frac{x^{5}}{0!}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\frac{243}{0!}$
104

Applicare la formula: $x!$$=x!$, dove $factx=0!$ e $x=0$

$\frac{x^{5}}{1}+\frac{3\left(5!\right)}{\left(1!\right)\left(4!\right)}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\frac{243}{0!}$
105

Applicare la formula: $x!$$=x!$, dove $factx=1!$ e $x=1$

$\frac{x^{5}}{1}+\frac{3\left(5!\right)}{1\cdot 24}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\frac{243}{0!}$
106

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$\frac{x^{5}}{1}+\frac{3\cdot 120}{1\cdot 24}x^{4}+\frac{9\left(5!\right)}{\left(2!\right)\left(3!\right)}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\frac{243}{0!}$
107

Applicare la formula: $x!$$=x!$, dove $factx=2!$ e $x=2$

$\frac{x^{5}}{1}+\frac{3\cdot 120}{1\cdot 24}x^{4}+\frac{9\left(5!\right)}{2\cdot 6}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\frac{243}{0!}$
108

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$\frac{x^{5}}{1}+\frac{3\cdot 120}{1\cdot 24}x^{4}+\frac{9\cdot 120}{2\cdot 6}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\frac{243}{0!}$
109

Applicare la formula: $ab$$=ab$, dove $ab=1\cdot 24$, $a=1$ e $b=24$

$\frac{x^{5}}{1}+\frac{3\cdot 120}{24}x^{4}+\frac{9\cdot 120}{2\cdot 6}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\frac{243}{0!}$
110

Applicare la formula: $ab$$=ab$, dove $ab=3\cdot 120$, $a=3$ e $b=120$

$\frac{x^{5}}{1}+\frac{360}{24}x^{4}+\frac{9\cdot 120}{2\cdot 6}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\frac{243}{0!}$
111

Applicare la formula: $ab$$=ab$, dove $ab=2\cdot 6$, $a=2$ e $b=6$

$\frac{x^{5}}{1}+\frac{360}{24}x^{4}+\frac{9\cdot 120}{12}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\frac{243}{0!}$
112

Applicare la formula: $ab$$=ab$, dove $ab=9\cdot 120$, $a=9$ e $b=120$

$\frac{x^{5}}{1}+\frac{360}{24}x^{4}+\frac{1080}{12}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\frac{243}{0!}$
113

Applicare la formula: $\frac{a}{b}$$=\frac{a}{b}$, dove $a=360$, $b=24$ e $a/b=\frac{360}{24}$

$\frac{x^{5}}{1}+15x^{4}+\frac{1080}{12}x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\frac{243}{0!}$
114

Applicare la formula: $\frac{a}{b}$$=\frac{a}{b}$, dove $a=1080$, $b=12$ e $a/b=\frac{1080}{12}$

$\frac{x^{5}}{1}+15x^{4}+90x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\frac{243}{0!}$
115

Applicare la formula: $\frac{x}{1}$$=x$, dove $x=x^{5}$

$x^{5}+15x^{4}+90x^{3}+\frac{27\left(5!\right)}{\left(3!\right)\left(2!\right)}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\frac{243}{0!}$
116

Applicare la formula: $x!$$=x!$, dove $factx=3!$ e $x=3$

$x^{5}+15x^{4}+90x^{3}+\frac{27\left(5!\right)}{6\cdot 2}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\frac{243}{0!}$
117

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$x^{5}+15x^{4}+90x^{3}+\frac{27\cdot 120}{6\cdot 2}x^{2}+\frac{81\left(5!\right)}{\left(4!\right)\left(1!\right)}x+\frac{243}{0!}$
118

Applicare la formula: $x!$$=x!$, dove $factx=4!$ e $x=4$

$x^{5}+15x^{4}+90x^{3}+\frac{27\cdot 120}{6\cdot 2}x^{2}+\frac{81\left(5!\right)}{24\cdot 1}x+\frac{243}{0!}$
119

Applicare la formula: $x!$$=x!$, dove $factx=5!$ e $x=5$

$x^{5}+15x^{4}+90x^{3}+\frac{27\cdot 120}{6\cdot 2}x^{2}+\frac{81\cdot 120}{24\cdot 1}x+\frac{243}{0!}$
120

Applicare la formula: $x!$$=x!$, dove $factx=0!$ e $x=0$

$x^{5}+15x^{4}+90x^{3}+\frac{27\cdot 120}{6\cdot 2}x^{2}+\frac{81\cdot 120}{24\cdot 1}x+\frac{243}{1}$
121

Applicare la formula: $ab$$=ab$, dove $ab=6\cdot 2$, $a=6$ e $b=2$

$x^{5}+15x^{4}+90x^{3}+\frac{27\cdot 120}{12}x^{2}+\frac{81\cdot 120}{24\cdot 1}x+\frac{243}{1}$
122

Applicare la formula: $ab$$=ab$, dove $ab=27\cdot 120$, $a=27$ e $b=120$

$x^{5}+15x^{4}+90x^{3}+\frac{3240}{12}x^{2}+\frac{81\cdot 120}{24\cdot 1}x+\frac{243}{1}$
123

Applicare la formula: $ab$$=ab$, dove $ab=24\cdot 1$, $a=24$ e $b=1$

$x^{5}+15x^{4}+90x^{3}+\frac{3240}{12}x^{2}+\frac{81\cdot 120}{24}x+\frac{243}{1}$
124

Applicare la formula: $ab$$=ab$, dove $ab=81\cdot 120$, $a=81$ e $b=120$

$x^{5}+15x^{4}+90x^{3}+\frac{3240}{12}x^{2}+\frac{9720}{24}x+\frac{243}{1}$
125

Applicare la formula: $\frac{a}{b}$$=\frac{a}{b}$, dove $a=3240$, $b=12$ e $a/b=\frac{3240}{12}$

$x^{5}+15x^{4}+90x^{3}+270x^{2}+\frac{9720}{24}x+\frac{243}{1}$
126

Applicare la formula: $\frac{a}{b}$$=\frac{a}{b}$, dove $a=9720$, $b=24$ e $a/b=\frac{9720}{24}$

$x^{5}+15x^{4}+90x^{3}+270x^{2}+405x+\frac{243}{1}$
127

Applicare la formula: $\frac{a}{b}$$=\frac{a}{b}$, dove $a=243$, $b=1$ e $a/b=\frac{243}{1}$

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

Réponse finale au problème

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

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