What does the distributive property combine to make multiplying whole numbers simpler

The distributive property in a given field combines multiplication with addition, that is in a field F, any elements a,b and c which satisfy the following rule:

a(b+c)=ab+ac

The whole numbers are a subset of the field R, which is composed of all rational and irrational numbers, hence the whole numbers satisfy this property. Therefore, if I wish to multiply 5 and 10, I can split this down to simplify the problem (or simply highlight the logical reasoning behind how long multiplication works.) To demonstrate:

5∗10=5∗(2+8)=5∗2+5∗8=10+40=50