Simplify: `(x^3-2x^2+3x-4)(x-1)-\ (2x-3)(x^2-x+1)`

Explanation

To simplify the expression \((x^3 - 2x^2 + 3x - 4)(x - 1) - (2x - 3)(x^2 - x + 1)\), we will follow these steps:

### Step 1: Expand the first part \((x^3 - 2x^2 + 3x - 4)(x - 1)\)

Using the distributive property (also known as the FOIL method for binomials), we multiply each term in the first polynomial by each term in the second polynomial:

\[
(x^3 - 2x^2 + 3x - 4)(x - 1) = x^3 \cdot x + x^3 \cdot (-1) - 2x^2 \cdot x - 2x^2 \cdot (-1) + 3x \cdot x + 3x \cdot (-1) - 4 \cdot x - 4 \cdot (-1)
...