Distributing and combining like terms, we have $a(2a+b)-2a^2+ab=2a^2+ab-2a^2+ab=2ab$. Now $a$ and $b$ are different prime numbers greater than 2, so $2ab=2^1\cdot a^1\cdot b^1$ has $(1+1)(1+1)(1+1)=\boxed{8}$ divisors.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Suppose $a$ and $b$ are different prime numbers greater than 2. How many whole-number divisors are there for the integer $a(2a+b)-2a^{2}+ab$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
8
Suppose $a$ and $b$ are different prime numbers greater than 2. How many whole-number divisors are there for the integer $a(2a+b)-2a^{2}+ab$?
test