Question

select the missing property.
$v + v + v + v$
$= 1v + 1v + 1v + 1v$ identity property of multiplication
$= (1 + 1 + 1 + 1)v$
$= 4v$ add

Explanation:

Step1: Recall the distributive property

The distributive property of multiplication over addition states that \(a(b + c)=ab + ac\), and in reverse, \(ab+ac=a(b + c)\). Here, we have \(1v+1v+1v+1v\), and we factor out the common factor \(v\) to get \((1 + 1+1 + 1)v\), which is the reverse of the distributive property (factoring form). So the property used here is the distributive property of multiplication over addition (or the distributive property for short, when applied in reverse for factoring).

Step2: Confirm the property

Looking at the step \(1v+1v+1v+1v=(1 + 1+1 + 1)v\), we are taking the common factor \(v\) out of each term \(1v\), which is exactly what the distributive property (in reverse) does. The identity property of multiplication was used in the first step to write \(v = 1v\), and now for combining the terms with the common factor \(v\), the distributive property (reverse) is used.

Answer:

Distributive property of multiplication over addition (or Distributive property)