Is there any way to show that the algebraic tensor product $A[[h]] \otimes A[[h]] \subsetneq (A \otimes A) [[h]]\ $?

Question

Let $A$ be a Hopf algebra over $k.$ Consider the formal power series $A[[h]]$ in $h$ over $A$ endowed with the $h$-adic topology. Then how do we show that $A[[h]] \otimes_{\text {alg}} A[[h]] \subsetneq (A \otimes_{\text {alg}} A) [[h]]\ $? More generally, how to show that the RHS is the completion of the LHS with respect to the $h$-adic topology?