1. **State the problem:** We want to find the expression for the area of a large rectangle with dimensions $2x - 2$ (top side) and $x + 1$ (left side), from which a smaller rectangle with dimensions $x$ (width) and $x - 2$ (height) is removed. 2. **Write the formula for the area of rectangles:** The area of a rectangle is given by multiplying its length by its width. 3. **Calculate the area of the large rectangle:** $$\text{Area}_{\text{large}} = (2x - 2)(x + 1)$$ 4. **Calculate the area of the smaller rectangle to be removed:** $$\text{Area}_{\text{small}} = x(x - 2)$$ 5. **Write the expression for the remaining area:** $$\text{Area}_{\text{remaining}} = (2x - 2)(x + 1) - x(x - 2)$$ 6. **Expand the products:** $$ (2x - 2)(x + 1) = 2x^2 + 2x - 2x - 2 $$ $$ x(x - 2) = x^2 - 2x $$ 7. **Substitute and simplify:** $$ 2x^2 + 2x - 2x - 2 - (x^2 - 2x) = 2x^2 + 2x - 2x - 2 - x^2 + 2x $$ 8. **Combine like terms:** $$ 2x^2 - x^2 + 2x - 2x + 2x - 2 = x^2 + 2x - 2 $$ **Final answer:** $$\boxed{x^2 + 2x - 2}$$ This expression represents the area of the large rectangle with the smaller rectangle removed.