Product states
Product states are those states that can be factored into individual qubit states. 1 In general, a product state of $n$ qubits can be written as $$(\alpha_{n-1}\ket 0 + \beta_{n-1}\ket1) \otimes \dots \otimes (\alpha_{1}\ket 0 + \beta_{1}\ket1) \otimes (\alpha_{0}\ket 0 + \beta_{0}\ket1).$$ This only has $2n$ amplitudes.
# Example
$$\begin{aligned}
\frac{1}{2}(\ket{00} - \ket{01} + \ket{10} - \ket{11}) &= \frac{1}{\sqrt 2}(\ket0 + \ket1) \otimes \frac{1}{\sqrt2}(\ket0 - \ket 1) \
&= \ket+ \otimes \ket- \
&= \ket+\ket-.
\end{aligned}$$
# Uses
A classical computer can efficiently store the amplitudes of product states. So, if Quantum Computers only used product states, they would be efficiently simulated by classical computers. But in reality, because of the Entangled states, Classical computers can’t simulate quantum computers efficiently.