11. \( (3 w-5 t)^{2}+w(7 w-8 t) \)

To expand the expression \( (3w - 5t)^{2} + w(7w - 8t) \), we can begin by unfolding each component. First, expand \( (3w - 5t)^{2} \): \[ (3w - 5t)^{2} = (3w)^{2} - 2(3w)(5t) + (5t)^{2} = 9w^{2} - 30wt + 25t^{2} \] Next, expand \( w(7w - 8t) \): \[ w(7w - 8t) = 7w^{2} - 8wt \] Now, combine both expansions: \[ 9w^{2} - 30wt + 25t^{2} + 7w^{2} - 8wt \] Combine like terms: \[ (9w^{2} + 7w^{2}) + (-30wt - 8wt) + 25t^{2} = 16w^{2} - 38wt + 25t^{2} \] So, the final simplified expression is: \[ \boxed{16w^{2} - 38wt + 25t^{2}} \]