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By the distributive property, this is equivalent to: $$x^2(x^2+2x+2)-2x(x^2+2x+2)+2(x^2+2x+2)$$Now, we can distribute in each of the above, and group like terms: $$x^4+2x^3+2x^2-2x^3-4x^2-4x+2x^2+4x+4$$$$\boxed{x^4+4}$$