Definition:Binomial Expansion

Definition

Consider the Binomial Theorem, which in one of its various forms is given here:

$\paren {1 + x}^\alpha = 1 + \dbinom \alpha 1 x + \dbinom \alpha 2 x^2 + \dbinom \alpha 3 x^3 + \cdots$

The above algebraic expansion is known as the binomial expansion.

Also see

• Results about binomial coefficients can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): binomial expansion
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): binomial theorem
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): binomial expansion
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): binomial theorem