Marion,
if you remember the distributive property is easy to remember if you think
multiplication distributes over addition
which can be written as
a(b+c) = ab + ac
If you take your all your equations it looks like you are trying to show distributive property using 3(19)
well in this case our a is 3
but we don't have our b or c
or do we
in A. you have the eqn 3(10) = 3(20)  3(1)
if we assume that 20 is b and 1 is c
then we would have 3(20 + (1)) = 3(20)  3(1) and (20+(1)) = 19
so A would be a correct usage of the distributive property
in B. you have (3)(20) + (3)(1) = 3(20+1) but 20 + 1 ≠ 19
so it wouldn't be a correct usage of the distributive property
for C and D you would need to do the same as I did above
Hope this helps
F
BTW you can find more examples for this property and others at Purple Math
Sep 24

Felice R.