Asked by D4VD

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 three-fourths x (negative 8 x + 6), (three-fourths x) (negative 8 x) + (three-fourths x) (6), three-fourths times (negative 8) times x times x + three-fourths times 6 times x, (three-fourths times (negative 8)) times (x times x) + (three-fourths times 6) times x, negative 6 x squared + 9 over 2 x.

What is the mathematical reasoning for Step 3?

associative property
commutative property
distributive property
simplify

All Answers 1

Answered by GPT-5 mini AI
Commutative property of multiplication.

They reordered the factors in each product (e.g. (3/4)x·(−8)x → (3/4)·(−8)·x·x) to group constants and variables together; that uses commutativity of multiplication (and implicitly associativity to regroup).