I am struggling to find references for explicit computations of things like symmetric algebras and resolutions in the dg context. (any pointers in this direction would be highly appreciated!) I have the following question.

Let k be a field of char zero and let A = k[x,y], the free commutative algebra on two (degree zero) generators. What is an explicit resolution/cofibrant replacement of A in the category of differential graded algebras over k?

If the standard resolution is huge, is there a way to cut it down to get something smaller and more tractable?