Let's simplify each expression step by step.
- For the expression \(4x + 8y - 2x + 2y\):
Combine like terms:
\[ (4x - 2x) + (8y + 2y) = 2x + 10y \]
So, the simplified expression is:
\[ \boxed{2x + 10y} \]
- For the expression \(10x^2 + 4 - 10x + 1 - 5x^2\):
Combine like terms:
- For \(x^2\) terms: \(10x^2 - 5x^2 = 5x^2\)
- For \(x\) terms: \(-10x\) (there is no other \(x\) term to combine with)
- For constant terms: \(4 + 1 = 5\)
Putting it all together:
\[ 5x^2 - 10x + 5 \]
So, the simplified expression is:
\[ \boxed{5x^2 - 10x + 5} \]
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