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