If $d$ is a fixed positive integer, let $\Lambda_N$ be a finite subset of $Z^d$, the lattice points of $\mathbb{R}^d$, with $\Lambda_N \uparrow Z^d$ and satisfying ...

Expanding brackets means multiplying everything inside the bracket by the letter or number outside the bracket. For example, in the expression \(3(m + 7)\) both \(m\) and 7 must be multiplied by 3: ...