Final answer:
To model (2x² - 4x) and (x² - x - 1) with algebra tiles, 2 large squares represent 2x², and 4 negative rectangles represent -4x for the first expression. For the second expression, use 1 large square for x², 1 negative rectangle for -x, and 1 negative small square for -1.
Step-by-step explanation:
To model the algebraic expressions (2x² - 4x) and (x² - x - 1) using algebra tiles, we would represent each term with a corresponding tile. Generally, a large square represents x², a rectangle represents x, and a small square represents constants (numbers).
For the expression (2x² - 4x):
- You would use 2 large squares to represent the 2x².
- You would also use 4 rectangles; however, these rectangles would be flipped to the negative side to represent the -4x.
For the expression (x² - x - 1):
- You would use 1 large square to represent the x²
- You would use 1 rectangle, flipped to the negative side, to represent -x.
- Lastly, you would use 1 small square, also flipped to the negative side, to represent the -1.
These visual representations help illustrate how algebraic terms combine and interact.