How do you know whether to add or subtract when using distributive property to multiply?

Question

How do you know whether to add or subtract when using distributive property to multiply?

Answer 1

The complete name for The Distributive Property is:

    The Distributive Property of Multiplication Over Addition:     

                      a(b+c) = ab + ac

and

    The Distributive Property of Multiplication Over Subtraction:  

                      a(b-c) = ab - ac

 

Just to check your understanding:  Why isn't there a

     Distributive Property of Division Over Addition?          a/(b+c) = a/b - a/c   ????

     Distributive Property of Division Over Subtraction?     a/(b-c)  = a/b - a/c   ????

Answer 2

Let A, B and C be arbitrary numbers.

 

 

A × (B + C)  ---->  add

 

A × (B - C)  -----> subtract