Statement of The Theorem
According to the theorem, it is possible to expand any power of x + y into a sum of the form
where each is a specific positive integer known as binomial coefficient. This formula is also referred to as the Binomial Formula or the Binomial Identity. Using summation notation, it can be written as
The final expression follows from the previous one by the symmetry of x and y in the first expression, and by comparison it follows that the sequence of binomial coefficients in the formula is symmetrical.
A variant of the binomial formula is obtained by substituting 1 for y, so that it involves only a single variable. In this form, the formula reads
or equivalently
Read more about this topic: Binomial Theorem
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