1. Expand using the binomial theorm in powers of x up to and including x^3 : (1 + 2x + 3x^2)^5 : I always thought binomial theorm would be used to expand binomials... this is not a binomial unless i do htis [(1+2x) + (3x^2)^5]... now the problem comes when I simplifiy and collect like-terms because there will be a (1+2x)^5 and that is difficult to expand, is there a easier way or am I messing up somewhere?

2. General question here, "is there any real life uses for the binomial theorm and what the limitations... When shouldn't/can't you use it?"

this may seem obvious but after all binomial theorem are used to expand bionomials... that is one limitations, are there others or any real l ife use? please advice, thx alot guys.