Binomial Theorem
Method to expand polynomials
The binomial theorem states a formula for expressing the powers of sums. The most succinct version of this formula is shown immediately below.
Isaac Newton wrote a generalized form of the Binomial Theorem. However, for quite some time Pascal's Triangle had been well known as a way to expand binomials (Ironically enough, Pascal of the 17th century was not the first person to know about Pascal's triangle)
A closer look at the Binomial Theorem
The easiest way to understand the binomial theorem is to first just look at the pattern of polynomial expansions below.
 (x+y)² =x²+2xy + y²
 (x+y)^{3} = x^{3} + 3x^{2}Y+ 3xY^{2} + y^{3}
 (x+y)^{4}
=x^{4}+ 4x^{3}Y +6x^{2}Y^{2} + 4XY^{3} + Y^{4}
Binomial Theorem Formula
The generalized formula for the pattern above is known as the binomial theorem
Practice Problems on the Binomial Theorem
Practice Problem 2) Make use of the binomial theorem formula to determine the eleventh term in the expansion (2a − 2) ^{12}
