To expand the given expression, we will use the formula for squaring a binomial: (a+b)^2 = a^2 + 2ab + b^2.

First, expand (2a+3)^2:
(2a+3)^2 = (2a)^2 + 2(2a)(3) + 3^2
= 4a^2 + 12a + 9

Next, expand (3a+4)^2:
(3a+4)^2 = (3a)^2 + 2(3a)(4) + 4^2
= 9a^2 + 24a + 16

Finally, expand (5a-2)^2:
(5a-2)^2 = (5a)^2 + 2(5a)(-2) + (-2)^2
= 25a^2 - 20a + 4

Now, multiply all three expanded expressions together:
(4a^2 + 12a + 9)(9a^2 + 24a + 16)(25a^2 - 20a + 4)
Expanding this product will result in a lengthy polynomial expression.