Question

The table shows the multiplication of two linear expressions.

A 2-column table with 5 rows. First column is labeled Reason with entries Given, Step 1, Step 2, Step 3, Step 4. Second column is labeled Step with entries 2 m (three-halves minus 4 m), (2 m) (three-halves) + 2 m (negative 4 m), 2 times three-halves times m + 2 times (negative 4) times m times m, (2 times three-halves) times m + (2 times (negative 4)) times (m times m), 3 m minus 8 m squared.

What is the mathematical reasoning for Step 1?

associative property
commutative property
distributive property
simplify

Answer 1

Distributive property.

Reason: 2m·(3/2 − 4m) is expanded using a(b + c) = ab + ac, giving (2m)(3/2) + (2m)(−4m).