###### Exercise51

A student has (correctly) simplified an algebraic expression in the following steps. Between each pair of steps, identify the algebraic property that justifies moving from one step to the next.

\begin{equation*} \phantom{={}}{9\!\left(a+5\right)+9a} \end{equation*}

• commutative property of multiplication

• associative property of multiplication

• distributive property

\begin{equation*} ={\left(9a+45\right)+9a} \end{equation*}

• commutative property of multiplication

• associative property of multiplication

• distributive property

\begin{equation*} ={\left(45+9a\right)+9a} \end{equation*}

• commutative property of multiplication

• associative property of multiplication

• distributive property

\begin{equation*} ={45+\left(9a+9a\right)} \end{equation*}

• commutative property of multiplication

• associative property of multiplication

• distributive property

\begin{equation*} ={45+\left(9+9\right)a} \end{equation*}
\begin{equation*} ={45+18a} \end{equation*}