Question

select the missing property.
$7v + 7$
$= 7\cdot v + 7\cdot 1$ factor
$= 7(v + 1)$

Explanation:

Step1: Recall Distributive Property

The distributive property of multiplication over addition states that \( a(b + c)=a\cdot b + a\cdot c \), and the reverse (factoring) is \( a\cdot b + a\cdot c = a(b + c) \).

Step2: Identify the Property Used

In the step from \( 7\cdot v + 7\cdot 1 \) to \( 7(v + 1) \), we are using the reverse of the distributive property (factoring out the common factor 7), which is the distributive property (or more specifically, the distributive property of multiplication over addition in reverse, often called factoring using the distributive property).

Answer:

Distributive Property (or more precisely, factoring using the Distributive Property of Multiplication over Addition)