Using Parity operator for addition/subtraction

[guyvsdcsniper]

Homework Statement

Prove Πxf(r)+xΠfr)=0.
Compute Πxyf(r)-xyΠf(r):

Relevant Equations

Parity Operator

This is for a Quantum Mechanics class but part b of this question seemed like it relied more on math than physics so I think it appropriate to post here. If not, Mods please move to appropriate place.

For the $\Pi xf(\vec r)+x\Pi f(\vec r)=0$ I have my answer circled in red on the first image.
For $\Pi xyf(\vec r)-xy\Pi f(\vec r)$ I have my answer attached to the 2nd image.

Im not sure if I am approaching this correctly. I just followed the actions listed in the question, and it seems like the first part worked out so the same logic should apply to the 2nd part?

Looking to see If I have the right approach here or any feedback if available.

 

[WWGD]

Don't mean to nitpick, but you seem to have a parentheses missing on the second line; just left of )=0