Suppose
K
K
is a field and the
K
K
-algebra
A
A
is expressed as a tensor product of two quaternion algebras
A
≅
H
1
⊗
H
2
A \cong {H_1} \otimes {H_2}
. Let
N
i
{N_i}
be the norm form on
H
i
{H_i}
and define the "Albert form"
α
A
{\alpha _A}
to be the
6
6
-dimensional quadratic form determined by
α
A
⊥
⟨
1
,
−
1
⟩
≅
N
1
⊥
−
N
2
\alpha _{A} \bot \left \langle {1, - 1} \right \rangle \cong {N_1} \bot - {N_2}
. In [Adv. in Math. 48 (1983), 149-165] Jacobson proved: (1) any two Albert forms for
A
A
are similar; (2) if
A
A
and
B
B
are algebras of this type, then
A
≅
B
A \cong B
if and only if
α
A
{\alpha _A}
and
α
B
{\alpha _B}
are similar. The authors prove this result using quadratic forms and Clifford algebras, avoiding the application of Jacobson’s theory of Jordan norms.