Is binomial theorem just pascal's triangle? or is there another

Pascal's triangle is a visual representation of the coefficients involved in a binomial expansion. The th row of the triangle gives the coefficients of the terms in the expansion of .

The triangle itself looks like



and so on, while the expansions for are






and so on.

The binomial theorem says that





The numbers in the th row of the triangle are just , with .

So no, the binomial theorem and Pascal's triangle are not the same thing. Pascal's triangle is a way of organizing the pattern exhibited by the result of the binomial theorem.