Hey i've been working on this problem for a few days now, just seeing if anyone else has some insight.

∀x ∈ R, ∀ε ∈ R+, ∃δ ∈ R+, ∀y ∈ R, |x – y| < δ ==> |x^2 – y^2| < ε

prove using epsilon-delta structured proof

ive got to the point where

|x^2 – y^2| < δ|x + y|

but am not completely stuck, I think I have to replace y with a constant somehow? any help would be great! thanks in advance!