Is it possible to have $x^Tyx^TAx=x^T(yx^T)^TAx$? where $x,y$ are vectors of equal dimensions and $A$ is a matrix

Question

Can one write, $x^Tyx^TAx=x^T(yx^T)^TAx$? where $x,y\in\mathbb{R}^n$ and $A\in\mathbb{R}^{n\times n}$ or in other words, is it possible to write: $x^TBAx=x^TB^TAx$? where $B\in\mathbb{R}^{n\times n}$?