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^= 81a^2 - 72ac + 16c^2
(9a+4c)(4c-9a) = 36c^2 - 81a^2 - 36ac + 81a= 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 + 4a= 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^= -68ac - 20c^2 + 71a= 3ac - 20c^2
Therefore, (9а-4с)^2-(9а+4с)(4с-9а)+71ас-162a^2 simplifies to 3ac - 20c^2.
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^
= 81a^2 - 72ac + 16c^2
(9a+4c)(4c-9a) = 36c^2 - 81a^2 - 36ac + 81a
= 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 + 4a
= 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^
= -68ac - 20c^2 + 71a
= 3ac - 20c^2
Therefore, (9а-4с)^2-(9а+4с)(4с-9а)+71ас-162a^2 simplifies to 3ac - 20c^2.