Please help in to understand why/how $|\vec{a} +\vec{b}|^2 = |\vec{a}|^2 +|\vec{b}|^2 + 2 \vec{a}\cdot \vec{b}$
My precise confusion is why the modulus is not included in $2 \vec{a}\cdot \vec{b}$ ?
Since if we do $(|\vec{a}| +|\vec{b}|)^2$, we have modulus sign in every $\vec{a}$ and $\vec{b}$.