Long maximum

Algebra Level 5

Let x,yx, y be real numbers satisfying x+y=3x+y = 3. To 2 decimal places, what is the maximum value of

x4y+x3y+x2y+xy+xy2+xy3+xy4?x^4 y + x^3 y + x^2 y + x y + x y^2 + x y^3 + x y^4 ?


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