Question

select the missing property.
2(2y)
= (2·2)y
= 4y \tmultiply

Explanation:

Step1: Recall properties of multiplication

The equation \(2(2y)=(2\cdot2)y\) shows that we are regrouping the factors when multiplying. The property that allows us to regroup the factors in a multiplication expression is the Associative Property of Multiplication. The Associative Property of Multiplication states that for any real numbers \(a\), \(b\), and \(c\), \(a(bc)=(ab)c\). In this case, \(a = 2\), \(b=2\), and \(c = y\), so \(2(2y)=(2\cdot2)y\) follows the Associative Property of Multiplication.

Step2: Identify the property

From the step \(2(2y)=(2\cdot2)y\), we can see that we are associating (grouping) the first two numbers \(2\) and \(2\) together while multiplying with \(y\). So the missing property is the Associative Property of Multiplication.

Answer:

Associative Property of Multiplication