To simplify this expression, we will first expand and then combine like terms.

(9a-4c)^2 = (9a-4c)(9a-4c)
= 81a^2 - 36ac - 36ac + 16c^2
= 81a^2 - 72ac + 16c^2

(9a+4c)(4c-9a) = 36c^2 - 81a^2 - 36ac + 81ac
= 36c^2 - 81a^2 - 4ac

Combining the above two expressions, we get:

(9а-4с)^2-(9а+4с)(4с-9а)
= 81a^2 - 72ac + 16c^2 - (36c^2 - 81a^2 - 4ac)
= 81a^2 - 72ac + 16c^2 - 36c^2 + 81a^2 + 4ac
= 162a^2 - 68ac - 20c^2

Next, we add the rest of the terms:

71ac - 162a^2

Now, we combine all the terms:

(162a^2 - 68ac - 20c^2) + (71ac - 162a^2)
= 162a^2 - 68ac - 20c^2 + 71ac - 162a^2
= -68ac - 20c^2 + 71ac
= 3ac - 20c^2

Therefore, (9а-4с)^2-(9а+4с)(4с-9а)+71ас-162a^2 simplifies to 3ac - 20c^2.