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Binomial Theorem Calculator

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1

Solved example of binomial theorem

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

We can expand the expression $\left(x+3\right)^5$ using Newton's binomial theorem, which is a formula that allow us to find the expanded form of a binomial raised to a positive integer $n$. The formula is as follows: $\displaystyle(a\pm b)^n=\sum_{k=0}^{n}\left(\begin{matrix}n\\k\end{matrix}\right)a^{n-k}b^k=\left(\begin{matrix}n\\0\end{matrix}\right)a^n\pm\left(\begin{matrix}n\\1\end{matrix}\right)a^{n-1}b+\left(\begin{matrix}n\\2\end{matrix}\right)a^{n-2}b^2\pm\dots\pm\left(\begin{matrix}n\\n\end{matrix}\right)b^n$
The number of terms resulting from the expansion always equals $n + 1$. The coefficients $\left(\begin{matrix}n\\k\end{matrix}\right)$ are combinatorial numbers which correspond to the nth row of the Tartaglia triangle (or Pascal's triangle). In the formula, we can observe that the exponent of $a$ decreases, from $n$ to $0$, while the exponent of $b$ increases, from $0$ to $n$. If one of the binomial terms is negative, the positive and negative signs alternate.

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

Calculate the power $3^{0}$

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

Calculate the power $3^{1}$

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

Calculate the power $3^{2}$

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

Calculate the power $3^{3}$

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

Calculate the power $3^{4}$

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

Calculate the power $3^{5}$

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

Calculate the binomial coefficient $\left(\begin{matrix}5\\0\end{matrix}\right)$ applying the formula: $\left(\begin{matrix}n\\k\end{matrix}\right)=\frac{n!}{k!(n-k)!}$

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

Calculate the binomial coefficient $\left(\begin{matrix}5\\1\end{matrix}\right)$ applying the formula: $\left(\begin{matrix}n\\k\end{matrix}\right)=\frac{n!}{k!(n-k)!}$

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

Calculate the binomial coefficient $\left(\begin{matrix}5\\2\end{matrix}\right)$ applying the formula: $\left(\begin{matrix}n\\k\end{matrix}\right)=\frac{n!}{k!(n-k)!}$

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

Calculate the binomial coefficient $\left(\begin{matrix}5\\3\end{matrix}\right)$ applying the formula: $\left(\begin{matrix}n\\k\end{matrix}\right)=\frac{n!}{k!(n-k)!}$

$1x^{5}\frac{5!}{\left(0!\right)\left(5+0\right)!}+3x^{4}\frac{5!}{\left(1!\right)\left(5-1\right)!}+9x^{3}\frac{5!}{\left(2!\right)\left(5-2\right)!}+27x^{2}\frac{5!}{\left(3!\right)\left(5-3\right)!}+\left(\begin{matrix}5\\4\end{matrix}\right)\cdot 81x^{1}+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243x^{0}$
13

Calculate the binomial coefficient $\left(\begin{matrix}5\\4\end{matrix}\right)$ applying the formula: $\left(\begin{matrix}n\\k\end{matrix}\right)=\frac{n!}{k!(n-k)!}$

$1x^{5}\frac{5!}{\left(0!\right)\left(5+0\right)!}+3x^{4}\frac{5!}{\left(1!\right)\left(5-1\right)!}+9x^{3}\frac{5!}{\left(2!\right)\left(5-2\right)!}+27x^{2}\frac{5!}{\left(3!\right)\left(5-3\right)!}+81x^{1}\frac{5!}{\left(4!\right)\left(5-4\right)!}+\left(\begin{matrix}5\\5\end{matrix}\right)\cdot 243x^{0}$
14

Calculate the binomial coefficient $\left(\begin{matrix}5\\5\end{matrix}\right)$ applying the formula: $\left(\begin{matrix}n\\k\end{matrix}\right)=\frac{n!}{k!(n-k)!}$

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

Subtract the values $5$ and $-1$

$1x^{5}\frac{5!}{\left(0!\right)\left(5+0\right)!}+3x^{4}\frac{5!}{\left(1!\right)\left(4!\right)}+9x^{3}\frac{5!}{\left(2!\right)\left(5-2\right)!}+27x^{2}\frac{5!}{\left(3!\right)\left(5-3\right)!}+81x^{1}\frac{5!}{\left(4!\right)\left(5-4\right)!}+243x^{0}\frac{5!}{\left(5!\right)\left(5-5\right)!}$
16

Subtract the values $5$ and $-2$

$1x^{5}\frac{5!}{\left(0!\right)\left(5+0\right)!}+3x^{4}\frac{5!}{\left(1!\right)\left(4!\right)}+9x^{3}\frac{5!}{\left(2!\right)\left(3!\right)}+27x^{2}\frac{5!}{\left(3!\right)\left(5-3\right)!}+81x^{1}\frac{5!}{\left(4!\right)\left(5-4\right)!}+243x^{0}\frac{5!}{\left(5!\right)\left(5-5\right)!}$
17

Subtract the values $5$ and $-3$

$1x^{5}\frac{5!}{\left(0!\right)\left(5+0\right)!}+3x^{4}\frac{5!}{\left(1!\right)\left(4!\right)}+9x^{3}\frac{5!}{\left(2!\right)\left(3!\right)}+27x^{2}\frac{5!}{\left(3!\right)\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(5-4\right)!}+243x^{0}\frac{5!}{\left(5!\right)\left(5-5\right)!}$
18

Subtract the values $5$ and $-4$

$1x^{5}\frac{5!}{\left(0!\right)\left(5+0\right)!}+3x^{4}\frac{5!}{\left(1!\right)\left(4!\right)}+9x^{3}\frac{5!}{\left(2!\right)\left(3!\right)}+27x^{2}\frac{5!}{\left(3!\right)\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(5-5\right)!}$
19

Subtract the values $5$ and $-5$

$1x^{5}\frac{5!}{\left(0!\right)\left(5+0\right)!}+3x^{4}\frac{5!}{\left(1!\right)\left(4!\right)}+9x^{3}\frac{5!}{\left(2!\right)\left(3!\right)}+27x^{2}\frac{5!}{\left(3!\right)\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
20

Add the values $5$ and $0$

$1x^{5}\frac{5!}{\left(0!\right)\left(5!\right)}+3x^{4}\frac{5!}{\left(1!\right)\left(4!\right)}+9x^{3}\frac{5!}{\left(2!\right)\left(3!\right)}+27x^{2}\frac{5!}{\left(3!\right)\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
21

The factorial of $0$ is $1$

$1x^{5}\frac{5!}{1\left(5!\right)}+3x^{4}\frac{5!}{\left(1!\right)\left(4!\right)}+9x^{3}\frac{5!}{\left(2!\right)\left(3!\right)}+27x^{2}\frac{5!}{\left(3!\right)\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
22

The factorial of $5$ is $120$

$1x^{5}\frac{5!}{1\cdot 120}+3x^{4}\frac{5!}{\left(1!\right)\left(4!\right)}+9x^{3}\frac{5!}{\left(2!\right)\left(3!\right)}+27x^{2}\frac{5!}{\left(3!\right)\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
23

The factorial of $5$ is $120$

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

The factorial of $1$ is $1$

$1x^{5}\frac{120}{1\cdot 120}+3x^{4}\frac{5!}{1\left(4!\right)}+9x^{3}\frac{5!}{\left(2!\right)\left(3!\right)}+27x^{2}\frac{5!}{\left(3!\right)\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
25

The factorial of $4$ is $24$

$1x^{5}\frac{120}{1\cdot 120}+3x^{4}\frac{5!}{1\cdot 24}+9x^{3}\frac{5!}{\left(2!\right)\left(3!\right)}+27x^{2}\frac{5!}{\left(3!\right)\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
26

The factorial of $5$ is $120$

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

The factorial of $2$ is $2$

$1x^{5}\frac{120}{1\cdot 120}+3x^{4}\frac{120}{1\cdot 24}+9x^{3}\frac{5!}{2\left(3!\right)}+27x^{2}\frac{5!}{\left(3!\right)\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
28

The factorial of $3$ is $6$

$1x^{5}\frac{120}{1\cdot 120}+3x^{4}\frac{120}{1\cdot 24}+9x^{3}\frac{5!}{2\cdot 6}+27x^{2}\frac{5!}{\left(3!\right)\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
29

The factorial of $5$ is $120$

$1x^{5}\frac{120}{1\cdot 120}+3x^{4}\frac{120}{1\cdot 24}+9x^{3}\frac{120}{2\cdot 6}+27x^{2}\frac{5!}{\left(3!\right)\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
30

The factorial of $3$ is $6$

$1x^{5}\frac{120}{1\cdot 120}+3x^{4}\frac{120}{1\cdot 24}+9x^{3}\frac{120}{2\cdot 6}+27x^{2}\frac{5!}{6\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
31

Multiply $1$ times $120$

$1x^{5}\frac{120}{120}+3x^{4}\frac{120}{1\cdot 24}+9x^{3}\frac{120}{2\cdot 6}+27x^{2}\frac{5!}{6\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
32

Multiply $1$ times $24$

$1x^{5}\frac{120}{120}+3x^{4}\frac{120}{24}+9x^{3}\frac{120}{2\cdot 6}+27x^{2}\frac{5!}{6\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
33

Multiply $2$ times $6$

$1x^{5}\frac{120}{120}+3x^{4}\frac{120}{24}+9x^{3}\frac{120}{12}+27x^{2}\frac{5!}{6\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
34

Divide $120$ by $120$

$1\cdot 1x^{5}+3x^{4}\frac{120}{24}+9x^{3}\frac{120}{12}+27x^{2}\frac{5!}{6\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
35

Divide $120$ by $24$

$1\cdot 1x^{5}+5\cdot 3x^{4}+9x^{3}\frac{120}{12}+27x^{2}\frac{5!}{6\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
36

Divide $120$ by $12$

$1\cdot 1x^{5}+5\cdot 3x^{4}+10\cdot 9x^{3}+27x^{2}\frac{5!}{6\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
37

Multiply $1$ times $1$

$1x^{5}+5\cdot 3x^{4}+10\cdot 9x^{3}+27x^{2}\frac{5!}{6\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
38

Multiply $5$ times $3$

$1x^{5}+15x^{4}+10\cdot 9x^{3}+27x^{2}\frac{5!}{6\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
39

Multiply $10$ times $9$

$1x^{5}+15x^{4}+90x^{3}+27x^{2}\frac{5!}{6\left(2!\right)}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
40

The factorial of $2$ is $2$

$1x^{5}+15x^{4}+90x^{3}+27x^{2}\frac{5!}{6\cdot 2}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
41

The factorial of $5$ is $120$

$1x^{5}+15x^{4}+90x^{3}+27x^{2}\frac{120}{6\cdot 2}+81x^{1}\frac{5!}{\left(4!\right)\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
42

The factorial of $4$ is $24$

$1x^{5}+15x^{4}+90x^{3}+27x^{2}\frac{120}{6\cdot 2}+81x^{1}\frac{5!}{24\left(1!\right)}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
43

The factorial of $1$ is $1$

$1x^{5}+15x^{4}+90x^{3}+27x^{2}\frac{120}{6\cdot 2}+81x^{1}\frac{5!}{24\cdot 1}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
44

The factorial of $5$ is $120$

$1x^{5}+15x^{4}+90x^{3}+27x^{2}\frac{120}{6\cdot 2}+81x^{1}\frac{120}{24\cdot 1}+243x^{0}\frac{5!}{\left(5!\right)\left(0!\right)}$
45

The factorial of $5$ is $120$

$1x^{5}+15x^{4}+90x^{3}+27x^{2}\frac{120}{6\cdot 2}+81x^{1}\frac{120}{24\cdot 1}+243x^{0}\frac{5!}{120\left(0!\right)}$
46

The factorial of $0$ is $1$

$1x^{5}+15x^{4}+90x^{3}+27x^{2}\frac{120}{6\cdot 2}+81x^{1}\frac{120}{24\cdot 1}+243x^{0}\frac{5!}{120\cdot 1}$
47

The factorial of $5$ is $120$

$1x^{5}+15x^{4}+90x^{3}+27x^{2}\frac{120}{6\cdot 2}+81x^{1}\frac{120}{24\cdot 1}+243x^{0}\frac{120}{120\cdot 1}$
48

Multiply $6$ times $2$

$1x^{5}+15x^{4}+90x^{3}+27x^{2}\frac{120}{12}+81x^{1}\frac{120}{24\cdot 1}+243x^{0}\frac{120}{120\cdot 1}$
49

Multiply $24$ times $1$

$1x^{5}+15x^{4}+90x^{3}+27x^{2}\frac{120}{12}+81x^{1}\frac{120}{24}+243x^{0}\frac{120}{120\cdot 1}$
50

Multiply $120$ times $1$

$1x^{5}+15x^{4}+90x^{3}+27x^{2}\frac{120}{12}+81x^{1}\frac{120}{24}+243x^{0}\frac{120}{120}$
51

Divide $120$ by $12$

$1x^{5}+15x^{4}+90x^{3}+10\cdot 27x^{2}+81x^{1}\frac{120}{24}+243x^{0}\frac{120}{120}$
52

Divide $120$ by $24$

$1x^{5}+15x^{4}+90x^{3}+10\cdot 27x^{2}+5\cdot 81x^{1}+243x^{0}\frac{120}{120}$
53

Divide $120$ by $120$

$1x^{5}+15x^{4}+90x^{3}+10\cdot 27x^{2}+5\cdot 81x^{1}+1\cdot 243x^{0}$
54

Multiply $10$ times $27$

$1x^{5}+15x^{4}+90x^{3}+270x^{2}+5\cdot 81x^{1}+1\cdot 243x^{0}$
55

Multiply $5$ times $81$

$1x^{5}+15x^{4}+90x^{3}+270x^{2}+405x^{1}+1\cdot 243x^{0}$
56

Multiply $1$ times $243$

$1x^{5}+15x^{4}+90x^{3}+270x^{2}+405x^{1}+243x^{0}$
57

Any expression to the power of $1$ is equal to that same expression

$1x^{5}+15x^{4}+90x^{3}+270x^{2}+405x+243x^{0}$
58

Any expression multiplied by $1$ is equal to itself

$x^{5}+15x^{4}+90x^{3}+270x^{2}+405x+243x^{0}$
59

Any expression (except $0$ and $\infty$) to the power of $0$ is equal to $1$

$x^{5}+15x^{4}+90x^{3}+270x^{2}+405x+243\cdot 1$
60

Multiply $243$ times $1$

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

Final Answer

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

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