Beginning Algebra With Applications, Chapter 2, Review Exercises, Section Review Exercises, Problem 10

Simplify $3[2x - 3 (x - 2y)] + 3y$

$
\begin{equation}
\begin{aligned}
&= 3[2x + (-3)(x) - (-3)(2y)] + 3y && \text{Use the Associative Property of Multiplication to group factors}\\
\\
&= 3[2x + (-3)(x) + (3\cdot 2)y] + 3y && \text{Use the Associative Property of Multiplication to group factors}\\
\\
&= 3[2x - 3x + 6y] + 3y && \text{Evaluate}\\
\\
&= 3[-x + 6y] + 3y && \text{Combine like terms}\\
\\
&= 3(-x) + 3(6y) + 3y && \text{Use the Distributive Property}\\
\\
&= (3 \cdot (-1)) x + (3 \cdot 6)y + 3y && \text{Again by using the Associative Property of Multiplication to group factors}\\
\\
&= -3x + 18y + 3y && \text{Simplify}\\
\\
&= -3x + 21y && \text{Combine like terms}
\end{aligned}
\end{equation}
$