Give proper reasoning

Dear Student,
A symmetric function is a one which has same value if we put

α i n p l a c e o f β a n d β i n p l a c e o f α .

So, If we do the same for

f (α, β) = α^{2} β + α β^{2} t h e n w e g e t f (β, α) = β^{2} α + α^{2} β . S o, f (α, β) = f (β, α)

Hence it is symmetric.
Regards,