To expand the expression $2(x-1)(x-2)$, we can follow these steps:

1. Distribute the $(x - 1)$ with $(x - 2)$:

$(x - 1)(x - 2) = x(x - 2) - 1(x - 2)$

Expanding both terms:

$x(x - 2) = x^2 - 2x$ $-1(x - 2) = -x + 2$

So,

$(x - 1)(x - 2) = x^2 - 2x - x + 2 = x^2 - 3x + 2$

2. Now distribute the 2 across the result:

$2(x^2 - 3x + 2) = 2x^2 - 6x + 4$

Thus, the expanded form of the expression is:

$2x^2 - 6x + 4$

Would you like more details on this process? Or have any questions?

Here are some related questions:

1. What is the difference between factoring and expanding expressions?
2. How would you factor the quadratic expression $2x^2 - 6x + 4$?
3. What does the distributive property look like when applied to binomials?
4. Can you solve the quadratic equation $2x^2 - 6x + 4 = 0$?
5. What are the different methods to solve quadratic equations?

Tip: When expanding binomials, always keep track of signs and ensure every term is correctly multiplied.