Summary: In this paper, we prove the following two results. Let \(d\) be a natural number and \(q\), \(s\) be co-prime integers such that \(1<\mathit{qs}<|q|\). Then there exists a constant \(\delta>0\) depending only on \(q\), \(s\) and \(d\) such that for any finite subset \(A\) of \(\mathbb{R}^d\) that is not contained in a translate of a hyperplane, we have \[ |q\cdot A+s\cdot A|\geq(|q|+|s|+2d-2)|A|-O_{q,s,d}(|A|^{1-\delta}). \] The main term in this bound is sharp and improves upon an earlier result of A. Balog and G. Shakan [North-West. Eur. J. Math. 1, 57–67 (2015; Zbl 1397.11017)]. Secondly, let \(\mathcal{L}\in\operatorname{GL}_2(\mathbb{R})\) be a linear transformation such that \(\mathcal{L}\) does not have any invariant one-dimensional subspace of \(\mathbb{R}^2\). Then, for all finite subsets \(A\) of \(\mathbb{R}^2\), we have \[ |A+\mathcal{L}(A)|\geq 4|A|-O(|A|^{1-\delta}), \] for some absolute constant \(\delta >0\). The main term in this result is sharp as well.