The best exercise I've found to build the part of the tricep down by the elbow is one called Bodyweight Tricep Extensions.
The outer part of the tricep can be built with flared-elbow pushdowns. Instead of keeping your elbows in tight to your body and bringing the bar around in an arc, point your elbows out to the sides (flare) and push the bar straight down and bring it straight up.
Here are some other exercises that work the lower part of the triceps:
Tiger Bends: do a close-grip push-up with your feet up on a bench, lower yourself down flat onto your forearms then push-up.
French Curls: overhead barbell extensions on an incline bench. Bring the bar down behind your head.
Overhead Cable Extensions: use a high pulley. Stand facing away from the cable in a lunge position. Extend the bar forward overhead. This is a similar movement to both the French Curl and the Bodyweight Extensions.
Close Grip Presses to the Upper Chest: instead of pressing to the mid-chest as usual, lower the bar higher up on your chest.
Here are some exercises that work the outer triceps:
Flared-Elbow Pushdowns: do a pushdown as you would normally do, except keep your elbows out wide to the sides while doing them.
Reverse Grip One-Arm Pushdowns: keep your palm facing forward throughout the movement. Try to rotate your hand towards the outside as you are pushing down.
Flared-Elbow Close Grip Bench Press: point your elbows out to the sides during the close grip bench press movement..
Reverse-Grip Kickbacks: done with a palms-down grip. Again, try to rotate your hand towards the outside.
Bench Dips: place your hands beside your glutes on the bench. Let your elbows go out wide a little ways. To make the exercise harder, have a partner push down on your shoulders.
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