Singular Values & the SVD · Challenge problem

Find the maximum of $B(x, y) = 4x_1y_1 + 4x_1y_2 + 3x_2y_1 - 3x_2y_2$ over all unit vectors $x = (x_1, x_2)$ and $y = (y_1, y_2)$. Give your answer in simplest radical form.