When making a spell with an AoE effect, do I need to apply the AoE to each element of damage?

For instance if I were to create a cast on target spell:

Shock 7 points 7 seconds (in 10 ft)
Fire 7 points 7 seconds (in 10 ft)
Frost 7 points 7 seconds (in 10 feet)

Would I be able to reduce the spell cost by going:

Shock 7 points 7 seconds (in 10 ft)
Fire 7 points 7 seconds
Frost 7 points 7 seconds

With Shock being the dominant effect in this particular spell, as long as the Shock component has the AoE, do I actually need an AoE for the fire and frost to take effect?

The fire and frost will just be on target, so you will do big damage to one enemy, and lesser splash damage. Just look at 'enemies explode'.

Mmmph. You're right.

There was a moment there when I thought, "By damn - that might be an idea!" But you're right, and Enemies Explode is the proof of it.

Darn.