Question

identifying the properties that justify each step

Answer 1

We have the next multiplication properties

Line 1 to Line 2:

$\begin{gathered} (4x)(5y) \\ 4\cdot(x\cdot5)\cdot y \end{gathered}$

We can see that in this step is used the associative property of multiplication.

Line 2 to Line 3:

$\begin{gathered} 4\cdot(x\cdot5)\cdot y \\ 4\cdot(5\cdot x)\cdot y \end{gathered}$

We can see that in this step is used the commutative property of multiplication.

Line 3 to Line 4:

$\begin{gathered} 4\cdot(5\cdot x)\cdot y \\ (4\cdot5)(x\cdot y) \end{gathered}$

We can see that in this step is used again the associative property of multiplication