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:


*

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


The result you ask about, as Display name notes, is called the Binomial Theorem, and is a standard result. The Wikipedia page for it, unlike most, is actually quite useful.
