Question

Justifying Multiplication of Linear Expressions
A 2-column table with 5 rows. First column is labeled Step with entries negative 2 y (1.1 + y), (negative 2 y)(1.1) + (negative 2 y)(y), negative 2(1.1) y + (negative 2)(y)(y), ((negative 2)(1.1)) y + (negative 2)(y times y), negative 2.2 y minus 2 y squared. Second column is labeled Reason with entries given, 1, 2, 3, 4.

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


Reason 1:

Reason 2:

Reason 3:

Reason 4:

Answer 1

Reason 1: Distributive Property (a(b + c) = ab + ac).

Reason 2: Commutative Property of Multiplication (reorder factors: (−2y)(1.1) = −2·1.1·y and (−2y)(y) = −2·y·y).

Reason 3: Associative Property of Multiplication (regroup factors: −2·1.1·y = ((−2)(1.1))y and −2·y·y = (−2)(y·y)).

Reason 4: Simplify by multiplying and using exponents ( (−2)(1.1)=−2.2 and y·y = y^2 ), giving −2.2y − 2y^2.