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You have provided the factored form. It "expands" as follows.
(x^2 + 2x + 2)(x^2 - 2x + 2) = x^4 + 4
The expansion can be simplified by recognizing that you have the product of a sum and difference.
((x^2+2) + 2x)((x^2+2) - 2x)
= (x^2 + 2)^2 - (2x)^2
= x^4 + 4x^2 + 4 - 4x^2
= x^4 + 4
(x^2 + 2x + 2)(x^2 - 2x + 2) = x^4 + 4
The expansion can be simplified by recognizing that you have the product of a sum and difference.
((x^2+2) + 2x)((x^2+2) - 2x)
= (x^2 + 2)^2 - (2x)^2
= x^4 + 4x^2 + 4 - 4x^2
= x^4 + 4
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