Mashed Potatoes with vegetables

1 1/2 lbs russet potatoes , peeled, rinsed, cut into large chunks 3/4 lb carrot , trimmed, cut into 2-inch pieces 1 1/2 tablespoons unsalted butter , softened[...]

3 ears fresh corn or 1 cup frozen corn 1 lb yellow potato , peeled and cut in 1 inch cubes 1 lb red potatoes, peeled and cut in 1 inch cubes 3 medium carrots[...]

3 ears fresh corn or 1 cup frozen corn 1 lb yellow potato , peeled and cut in 1 inch cubes 1 lb red potatoes, peeled and cut in 1 inch cubes 3 medium carrots[...]