The problem asks us to expand and simplify the expression $(a-b)(2a-b)$.

1. Problem Description

The problem asks us to expand and simplify the expression $(a-b)(2a-b)$.

2. Solution Steps

To expand the expression $(a-b)(2a-b)$, we use the distributive property (also known as the FOIL method).

$(a-b)(2a-b) = a(2a-b) - b(2a-b)$

Now, we distribute $a$ and $-b$ over the terms in the parentheses:

$a(2a-b) = 2a^2 - ab$

$-b(2a-b) = -2ab + b^2$

Combining these two results, we have:

$2a^2 - ab - 2ab + b^2$

Now, we combine like terms:

$-ab - 2ab = -3ab$

So the simplified expression is:

$2a^2 - 3ab + b^2$

3. Final Answer

$2a^2 - 3ab + b^2$