Entangled States in Qubits: Product or Entangled?

[wam_mi]

Homework Statement

Suppose we define states [0] and [1] be the basis which [0] = (1,0) and [1] = (0,1).

There are two things I want to ask. Are the following states product or entangled states?

(i) [Xi] = \frac{1}{2} ([00] + [01] + [10] - [11])

(ii) [Xi] = \frac{1}{\sqrt{10}} ([01] + 3 [10])

Homework Equations

The Attempt at a Solution

I understand that [Xi] = \frac{1}{2} ([00] + [01] + [10] + [11]) is a product state, since it can be represented by the tensor products between two qubits. But I just can't see what the answers are for the questions I stated at above. Hm... I guess they're both entangled, am I wrong?

 

[gabbagabbahey]

A general two qubit product state is $|\Psi\rangle=(\alpha|0\rangle+\beta|1\rangle)\otimes(\gamma|0\rangle+\delta|1\rangle)$...Expand the tensor product and equate it to the state you wish to test... are there any values of $\alpha$, $\beta$, $\gamma$ and $\delta$ that make that equality hold?