Square a combinatorial formula (binomial theorem)

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I have the following function

$$ f(a,b,c\mid k) = \binom{k}{l}a^l\binom{k-l}{m}b^mc^{k-l-m}[1-d^m] $$ Upon application of the binomial theorem I get

$$ [a+b+c]-[a+bd+c] $$ I do not wish to simplify this further.

I would also like to consider $f^2$. It is at this point I am unsure how to proceed, starting from my original expression. How would I rationalise this?