Why is the distributive property important?

The distributive property says that ##a(b+c)=a*b+a*c##

Without this you wouldn't be able the expand expressions like:

##(x+1)(2x-4)## into

##x*2x+x*(-4)+1*2x+1*(-4)## and then

##2x^2-2x-4##

In other words, you would not be able to 'clear the brackets'