Let's simplify the given expression step by step:

(а+4в)^2 = а^2 + 8ав + 16в^2

(4в-3а)(4в+3а) = 16в^2 - 12ав + 12ав - 9а^2 = 16в^2 - 9а^2

а(3в+5а) = 3ав + 5а^2

Now substitute these simplified forms back into the original expression:

(а+4в)^2 - (4в-3а)(4в+3а) + а(3в+5а)
= (a^2 + 8ав + 16в^2) - (16v^2 - 9a^2) + (3av + 5a^2)
= а^2 + 8ав + 16в^2 - 16v^2 + 9а^2 + 3аv + 5а^2
= 15а^2 + 11ав + 16в^2 + 3аv

Therefore, the simplified form of the given expression is 15a^2 + 11av + 16v^2 + 3av.