Expand (1-x)^n and sub in x=1 for both that and (1+x)^n, finally add the 2 together and then continue to manipulate the eqn to show whatever needs to be proven
Substitute into the binomial equation call call it 1. Substitute into another binomial equation call call it 2. Add the 2 equations. Noting when you add an even number + odd number = odd number. The 'odd' binomial terms cancel and the 'even' terms are doubled. Hope that is a starting point.
Attached is a Latex suggestion. Also find attached are some binomial questions from a Pure Mathematics text book from the 1970s. It may NOT be what is required for the EX 1 syllabus, but great practice.