<s>[INST] Let $a$ and $b$ be the coefficient of $x^3$ in $(1+x+2x^2+3x^3)^4$ and $(1+x+2x^2+3x^3+4x^4)^4$ respectively. Let $a$ and $b$ be the coefficient of $x^3$ in $(1+x+2x^2+3x^3)^4$ and $(1+x+2x^2+3x^3+4x^4)^4$ respectively.Find $(a-b).$

I tried to factorize $(1+x+2x^2+3x^3)$ and $(1+x+2x^2+3x^3+4x^4)$ into product of two binomials,but i could not.And i do not have any other method to solve it.
 [/INST] The  problem is a way of making the point that changing the terms of degree $k$ and higher in the argument can only change the degree $k$-or-higher terms in the result, when applying polynomial or power-series operations (such as taking the 4th power of the argument).  If you are performing a calculation to get the answer, something is wrong.
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