My professor showed me a rule about the distributive property that I’ve read for years but have always overlooked.

We’ve all seen the classic a(b+c)

Apparently the distributive property only respects addition and subtraction. Which means that a(bc) is not distributive.

So if you have this problem:

0.01+2(0.01+0.03)=0.01

And you suddenly realized that you wanted to completely annihilate the zeroes by distributing 100 to both sides of the equation;

100[0.01+2(0.01+0.03)]=0.01(100)

What the hell would you do?

Keep in mind a(b+c) is the distributive property in a mathematical nutshell, and that this is a grade school question, so let’s look at the left side of the equation I.e the part I fucked up on I’m college algebra thanks to never encountering the scenario prior.

a=100

b=0.01

So what is c?

I wrote the answer in my notes but thanks to overestimating my damn memory I didn’t write the notes concisely enough.

Is “c” the product of 2(0.01+0.03)?

Or is “c” (0.01+0.03)?

Or is “c” a choice between “2” and “(0.01+0.03)”?

In other words, how do you properly distribute the 100?

Please help because this principle is so fucking basic that it could kill me in the future.