Question

Justifying Multiplication of Linear Expressions
A 2-column table with 4 rows. First column is labeled Step with entries 2 z (negative 8 z), 2 times (negative 8) times z times z, (2 times (negative 8)) times (z times z), negative 16 z squared. Second column is labeled Reason with entries given, 1, 2, 3.

The table shows the multiplication of two linear expressions. Select the correct reason for each step.


Reason 1:

Reason 2:

Reason 3:

Answer 1

Reason 1: Commutative property of multiplication (reorder the factors to 2·(−8)·z·z).

Reason 2: Associative property of multiplication (group constants and variables: (2·(−8))·(z·z)).

Reason 3: Simplify — multiply the coefficients and use z·z = z^2, giving −16z^2.