$V\subset A^n(k)$ and $W\subset A^m(k)$ are two algebraic sets. How can I show that $V\times W $ is algebraic set in $A^{m+n}(k)$?

Question

$V\subset A^n(k)$ and $W\subset A^m(k)$ are two algebraic sets. How can I show that $V\times W $ is algebraic set in $A^{m+n}(k)?$ where $A^n(k)$ is $k^n$ ($k$ is a field)

Answer 1

Hint : $V\times W=V\times A^m(k)\cap A^n(k)\times W$