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Binomial Theorem

If you’re like me — haven’t touched math/statistics in years but trying to tackle concepts for Machine Learning— here’s a really easy way to understand Binomial Theorem:

But maybe even reading the terms “Binomial” intimidate you. (I had flashing nightmares from my Calculus class four years ago

.)

The first thing you need to remember is that a polynomial is an expression. In simple English, think of polynomials as “sentences” that contain different “words”.

Depending on how many “words” the polynomial has, it has a different term.

Coefficient is the number before a variable (in this case “-3” is the coefficient, “x” is the variable). Degree

is the highest power of the variable.

Ok, now that “binomial”, “polynomial” and “coefficient” don’t sound as intimidating, let’s now figure out Binomial Theorem:

binomial theorem formula

I know, it looks horrible, but it’s not that bad.

Let’s use an example:

The theorem becomes easier to understand once you break down the answer into “a”s and “b”:

Now if we were to go back to the formula…

k will keep increasing (0 > 1 > 2 > 3) until it reaches 3.

a will keep decreasing as k increases (3–0 > 3–1 > 3–2 > 3–3).

b will keep increasing as k increases (0 > 1 > 2 > 3).

“3 choose k” is the coefficient that will change according to the value “k”.

Now all you have to do is get the sum of all the outcomes for when k=0, k=1, k=2, k=3.