First, let's simplify each part of the expression separately:

(7+2i)^2 = (7+2i)(7+2i)
Expanding using FOIL (First, Outer, Inner, Last):
= 77 + 72i + 2i7 + 2i2i
= 49 + 14i + 14i + 4i^2
= 49 + 28i + 4(-1)
= 49 + 28i - 4
= 45 + 28i

Next, let's simplify (6+8i)(6-8i):
= 66 + 6(-8i) + 8i6 + 8i*(-8i)
= 36 - 48i + 48i - 64i^2
= 36 - 64(-1)
= 36 + 64
= 100

Now, let's multiply the two simplified expressions:
(45 + 28i)*100
= 4500 + 2800i

Therefore, (7+2i)^2 (6+8i)(6-8i) = 4500 + 2800i.