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