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Simplifying
4x2 + 8xy + 4y2

Reorder the terms:
8xy + 4x2 + 4y2

Factor out the Greatest Common Factor (GCF), '4'.
4(2xy + x2 + y2)

Factor a trinomial.
4((x + y)(x + y))

Final result:
4(x + y)(x + y)
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