How does distributive property works?

Answer 1

Suppose x, y and z are elements of a set and # and ~ are two binary operations defined on the set. Then, the distributive property of # over ~ sates that for all elements x, y and z in the set,

x # (y ~ z) = x#y ~ x#z

A common example is # = multiplication and ~ = addition (or subtraction). In that case, the distributive property of multiplication over addition states that

x*(y + z) = x*y + x*z