Question 352568
5(2y-Z)^2 + 4(y+2Z)^2
= 5 [ 4y^2 + 4Zy + Z^2 ] + 4 [ y^2 + 4Zy + 4Z^2 ]
= 20y^2 + 20Zy + 5Z^2 + 4y^2 + 16Zy + 16Z^2
= 20y^2 + 4y^2 - 20Zy +16Zy + 5Z^2 + 16Z^2
= 24y^2 - 4Zy + 21Z^2

Perhaps you had did some careless mistakes in the process.