First, expand (sin²x+cos²x)²:
(sin²x+cos²x)² = sin⁴x + 2sin²xcos²x + cos⁴x
Now, subtract 2sin²xcos²x from the expanded term:
(sin⁴x + 2sin²xcos²x + cos⁴x) - 2sin²xcos²x= sin⁴x + 2sin²xcos²x + cos⁴x - 2sin²xcos²x= sin⁴x + cos⁴x
Therefore, the final expression is sin⁴x + cos⁴x.
First, expand (sin²x+cos²x)²:
(sin²x+cos²x)² = sin⁴x + 2sin²xcos²x + cos⁴x
Now, subtract 2sin²xcos²x from the expanded term:
(sin⁴x + 2sin²xcos²x + cos⁴x) - 2sin²xcos²x
= sin⁴x + 2sin²xcos²x + cos⁴x - 2sin²xcos²x
= sin⁴x + cos⁴x
Therefore, the final expression is sin⁴x + cos⁴x.