  We show that for a Banach algebra $A$ with a bounded approximate identity,
the amenability of the projective tensor product of A with A, the amenability
of the projective tensor product of A with A^{op}and the amenability of A are
equivalent. Also if A is a closed ideal in a commutative Banach algebra B, then
the weak amenability of the projective tensor product of A and B implies the
weak amenability of A.
