Solution
= Solution
The degree-$n$ component is
$$
(A\otimes_kB)_n=\bigoplus_{i+j=n}A_i\otimes_kB_j.
$$
Dimensions therefore satisfy the <Cauchy product> rule, giving
$$
P_{A\otimes_kB}(t)=P_A(t)P_B(t).
$$
= Solution
The degree-$n$ component is
$$
(A\otimes_kB)_n=\bigoplus_{i+j=n}A_i\otimes_kB_j.
$$
Dimensions therefore satisfy the <Cauchy product> rule, giving
$$
P_{A\otimes_kB}(t)=P_A(t)P_B(t).
$$