How does Pascal's triangle relate to binomial expansion?
1 Answer
It tells you the coefficients of the terms.
Explanation:
Let's consider the

#(a+b)^2 = a^2+2ab+b^2# . All terms are of degree two: The exponent of#a^2# is#2# , and the same goes for#b^2# , while in#2ab# , we have#ab=a^1b^1# , and so again#1+1=2# . 
#(a+b)^3 = a^3 + 3a^2b + 3ab^2+b^3# , and all terms are either cubic (#a^3# and#b^3# ), or the exponents of the variables sum up to three:#a^2b# and#ab^2# lead to#1+2=2+1=3# .
So, when expanding the power of a binomial, you must count how many possible combinations you have to find numbers
For example, the first line of the triangle is a simple
The second line is
The third line is
And so on: if you look above, you have that the coefficients of the cubic expansion are