Question 673284
WARNING:
Different books/teachers may give slightly different names to the same properties.
 
IF YOU MUST CHOOSE JUST ONE PROPERTY, AS IN A MULTIPLE CHOICE QUESTION,
then it would be simple.
I could say that {{{-29c}}} obviously means the additive inverse of {{{29c}}}.
Then I would say that
{{{29c + (-29c)=0}}} is the Additive Identity Property.
 
IF A FULL EXPLANATION IS EXPECTED,
it may be more complicated.
Unfortunately, I suspect they want to make it more complicated, and we would need to invoke 3 or more properties.
If it is interpreted as just {{{-29c=-29*c}}}, we could say that
{{{29c + (-29c)=(29+(-29))*c}}} is the application of the Distributive Property.
Then,
{{{(29+(-29))*c=0*c}}} Additive Identity Property,
and finally,
{{{0*c=0}}} Zero Property
 
IF THEY WANT TO MAKE YOU EXPLAIN EVEN MORE:
The Distributive Property is usually represented in the form
{{{c(a+b)=c*a+c*b}}}.
In this case we have {{{a*c+b*c=(a+b)c}}}, with {{{a=29}}} and {{{b=-29}}}.
That is usually referred to as "taking out a common factor".
{{{a*c+b*c=(a+b)c}}} is the same (read backwards) as
the usual {{{(a+b)c=a*c+b*c}}} distributive property.
{{{c(a+b)=c*a+c*b}}} and  {{{(a+b)c=a*c+b*c}}} are the same thing,
because of the Commutative Properties for Addition and Multiplication.