1. The problem is to simplify the expression $M = -2 \times (3,2 - 5,7) + 4 \times (1,6 - 3,1)$. 2. First, perform the subtraction inside each vector: $$(3,2) - (5,7) = (3-5, 2-7) = (-2, -5)$$ $$(1,6) - (3,1) = (1-3, 6-1) = (-2, 5)$$ 3. Now multiply each vector by the scalar: $$-2 \times (-2, -5) = (-2 \times -2, -2 \times -5) = (4, 10)$$ $$4 \times (-2, 5) = (4 \times -2, 4 \times 5) = (-8, 20)$$ 4. Finally, add the two resulting vectors: $$(4, 10) + (-8, 20) = (4 + (-8), 10 + 20) = (-4, 30)$$ 5. So, the simplified vector $M$ is $$\boxed{(-4, 30)}$$.