Symmetric Expression with a twist

Algebra Level 3

Consider all pairs of real numbers such that a+b=3 a + b = 3 .

What is the minimum value of

a2b22a2b2ab2+a2+4ab+b22a2b+1? a^2 b^2 - 2a^2 b - 2 a b^2 + a^2 + 4ab + b^2 - 2a - 2b + 1?

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