Newton's Third Law
Also called Third law of motion, Action and reaction
Newton's third law says that when two objects interact, each exerts a force on the other equal in magnitude and opposite in direction. The two forces of the pair act on different objects, which is why they never cancel each other.
Forces come in pairs because a force is an interaction, not a possession. AP Physics 1 essential knowledge 2.3.A.1 states it as the interaction of two objects in terms of the paired forces that each exerts on the other:
The pair never cancels. Cancellation requires two forces on the same object, and these two are on different objects by construction. A book on a table pushes down on the table and the table pushes up on the book; the up force on the book is balanced by the book's weight, which is a separate fact about a separate pair. Losing that distinction is the error the law produces most often, and the fix is mechanical: put the two forces on two free-body diagrams and see that they never appear together.
Nothing pushes itself. 2.2.A.1.ii says an object or system cannot exert a net force on itself, and 2.3.A.2 draws the consequence: interactions between objects inside a system, the internal forces, do not influence the motion of that system's center of mass. That is what lets you treat two carts pushing apart as one system and ignore the shove entirely.
The AP Physics 1 equation sheet prints no line for the third law. It is a statement about which forces exist, so it does its work when you build the diagram rather than when you substitute. How to draw a free-body diagram covers that step, and tension is the case where the pairing does most of the work.