As @epelaaez noted in their answer, by definition, a state is entangled if it cannot be expressed as the product of smaller qubit states. For example, $$ \frac{1}{2}\left(|00\rangle + |01\rangle + |10\rangle + |11\rangle\right) =\left[\frac{1}{\sqrt{2}}(|0 \rangle + |1 \rangle)\right]\left[\frac{1}{2}(|0 \rangle + |1 \rangle)\right]$$ is not entangled because it factors into the product of $\frac{1}{2}(|0 \rangle + |1 \rangle)$ with itself.

However, you cannot factor $\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)$ since $$\begin{aligned}\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle) &= \frac{1}{\sqrt{2}} (|a_0\rangle + |a_1\rangle)(|b_0\rangle + |b_1\rangle)\\ &= \frac{1}{\sqrt{2}} (|a_0b_0\rangle + |a_0b_1\rangle + |a_1b_0\rangle + |a_1b_1\rangle)\end{aligned}. $$ To get the $|00\rangle$ term, you need $a_0=0$ and either $b_0$ or $b_1$ to equal $0$ (with the other one not present): $$\frac{1}{\sqrt{2}} (|0\rangle + |a_1\rangle)(|0\rangle),$$ but then there is no way to get the $|11\rangle$ term from the factorization.

As @epelaaez noted in their answer, by definition, a state is entangled if it cannot be expressed as the product of smaller qubit states. For example, $$ \frac{1}{2}\left(|00\rangle + |01\rangle + |10\rangle + |11\rangle\right) =\left[\frac{1}{\sqrt{2}}(|0 \rangle + |1 \rangle)\right]\left[\frac{1}{\sqrt{2}}(|0 \rangle + |1 \rangle)\right]$$ is not entangled because it factors into the product of $\frac{1}{\sqrt{2}}(|0 \rangle + |1 \rangle)$ with itself.

However, you cannot factor $\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)$ since $$\begin{aligned}\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle) &= \frac{1}{\sqrt{2}} (|a_0\rangle + |a_1\rangle)(|b_0\rangle + |b_1\rangle)\\ &= \frac{1}{\sqrt{2}} (|a_0b_0\rangle + |a_0b_1\rangle + |a_1b_0\rangle + |a_1b_1\rangle)\end{aligned}. $$ To get the $|00\rangle$ term, you need $a_0=0$ and either $b_0$ or $b_1$ to equal $0$ (with the other one not present): $$\frac{1}{\sqrt{2}} (|0\rangle + |a_1\rangle)(|0\rangle),$$ but then there is no way to get the $|11\rangle$ term from the factorization.