Hi, Yes! Your factoring completely was good work

200w^2+640wg+512g^2 

8(25w^2 + 80wg + 64g^2)

8(5w + 8g)(5w + 8g) = 8(5w + 8g)^2

May check Your factoring using the FOIL Method

F	First terms 25w^2

O	Outside terms 40wg

I	Inside terms  40wg

L	Last terms    64g^2

 

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