SOLUTION: How do I simplify the expression and justify each step? By justify I mean each time you simplify would that step be distributive, associative, commutative etc. 29c + (-29c)

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Question 673284: How do I simplify the expression and justify each step? By justify I mean each time you simplify would that step be distributive, associative, commutative etc.
29c + (-29c)

Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
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 obviously means the additive inverse of .
Then I would say that
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 , we could say that
is the application of the Distributive Property.
Then,
Additive Identity Property,
and finally,
Zero Property

IF THEY WANT TO MAKE YOU EXPLAIN EVEN MORE:
The Distributive Property is usually represented in the form
.
In this case we have , with and .
That is usually referred to as "taking out a common factor".
is the same (read backwards) as
the usual distributive property.
and are the same thing,
because of the Commutative Properties for Addition and Multiplication.

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