Evaluate: (-(4x+2y^2-2y)+2x)\div2

Expression: $\left( -\left( 4x+2{y}^{2}-2y \right)+2x \right)\div2$

When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses

$\left( -4x-2{y}^{2}+2y+2x \right)\div2$

Collect like terms

$\left( -2x-2{y}^{2}+2y \right)\div2$

Write the division as a fraction

$\frac{ -2x-2{y}^{2}+2y }{ 2 }$

Factor out $2$ from the expression

$\frac{ 2\left( -x-{y}^{2}+y \right) }{ 2 }$

Cancel out the common factor $2$

$-x-{y}^{2}+y$