Are these polynomials irreducible in $\mathbb{R}[x,y]$?

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Is $(x^2-1)^2+(y^2-1)^2-1$ irreducible in $\mathbb{R}[x,y]$ ?

Is $(x^2-1)^2+(y^2-1)^2$ irreducible in $\mathbb{R}[x,y]$ ?