Beginning Algebra With Applications, Chapter 2, Review Exercises, Section Review Exercises, Problem 22

Simplify $-2[x - 2(x-y)] + 5y$

$\begin{equation} \begin{aligned} &=-2[x - 2(x) - (-2)(y)] + 5y && \text{Use the Distributive Property}\\ \\ &= -2[x -2x + 2y] + 5y && \text{Evaluate}\\ \\ &= -2[-x + 2y] + 5y && \text{Evaluate}\\ \\ &= -2[-x + 2y] + 5y && \text{Combine like terms}\\ \\ &= (-2)(-x) + (-2)(2y) + 5y && \text{Again by using the Distributive Property}\\ \\ &= ((-2) \cdot (-1))x - (2 \cdot 2)y + 5y && \text{Use the Associative Property of Multiplication to group factors}\\ \\ &= 2x -4y + 4y && \text{Evaluate}\\ \\ &= 2x + y && \text{Combine like terms} \end{aligned} \end{equation}$