Discrete Math/Calculus (Given summation formula, find value of x) Textbook Question:
Given $\sum\limits_{i=0}^\mathbb{50}{50\choose i}8^i $ = $x^{100}$ . Find the values of x ?
Textbook Solution:
$\sum\limits_{i=0}^\mathbb{50}{50\choose i}8^i $ = $(1+8)^{50} = 9^{50} = [(+-3)^2)]^{50}$ 
$\therefore$ x = +-3
Personal Logical Question:


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*In the given textbook solution, how is $(1+8)^{50}$ obtained?


The book is using Binomial Theorem:
$$\sum_{i=0}^{n}{n \choose i}a^ib^{n-i}=(a+b)^{n}$$
Use $a=8$, $b=1$ and $n=50$.
