authorea.com/100622

Pascal’s triangle is filled with patterns that can solve
many mathematical problems. One of the neat things that the triangle can do is help with
binomial expressions. First let’s take a look at binomial expressions. Binomial expressions relate to the sum or difference of two
terms such as:

\(x+2\)

\(3x+5\)

\(c-d\)

Raising these expressions to powers of two can actually be
pretty easy, for example:

\(\left(x+2\right)^2=x^2+2x+2x+4\) which then equals \(x^2+4x+4\). Yay we did it! Pretty easy. Now let’s try to take the binomial expression \(x+y\) and raise it to the 4th power. Do we really want to do that by hand? Of course it can be done by hand but it is very tedious work. This is where Pascal’s triangle comes in handy.

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