Answer:
This is already as simple as it will get. You could expand it though. In that case you'd get:
(x + y)⁴
= (x² + 2xy + y²)²
= x⁴ + 2x³y + x²y² + 2x³y + 4x²y² + 2xy³ + x²y² + 2xy³ + y⁴
= x⁴ + 4x³y + 6x²y² +4xy³ + y⁴
But this doesn't simplify at all.