Binomial Theorem
Method to expand polynomials
The binomial theorem states a formula for expressing the powers of sums. The most succint version of this formula is the 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 = x3 + 3x2Y+ 3xY2 + y3
- (x+y)4
=x4+ 4x3Y +6x2Y2 + 4XY3 + Y4
The generalized formula for the pattern above is
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