Keep in mind, if you use a chemical to kill the plant, you run the risk of killing other plants it comes in contact with. This includes drift of the chemical on leaves and roots soaking it up.
That being said, each invasive plant may need it's own game plan. For example, if it is Japanese Honeysuckle, timing is everything. Here's a great resource to get started and to help you select the right herbicide for your specific need.
Be sure to follow the directions on the products you use.
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