What happens when we multiply A by A*B? Does B get affected?

Answer 1

I'm guessing what you mean is: Does A* (AB) = (AABA)?

In that case, no, B does not get "affected".

Due to the order of operations, it doesn't matter what order you multiply A and B.

A * (AB) = A * A * B = A^2 * B

(These all mean the same thing, just in different forms)

Let's check this by replacing A and B with variables. A=3 , B=5

3 * (3*5) = 3*3*5 = 3^2 * 5 = 45

Answer checks out.

Answer 2

The formula would essentially look like this A*(AB). So when you solve for the answer you get (A^2)*B. So it is the same answer, just a different notation.

For example:

If A=2 and B=3

Then:

2*(2*3)=2*(6)=12

(2^2)*3=(4)*3=12

This is known as the associative property of multiplication. It means the mode of grouping the factors does not change the result of the multiplication. Basically it doesn't matter what order you put the terms in, if they are all multiplied by each other than the answer is the same.