1. The problem asks to find an equivalent representation of the sum of two polynomials: $$(x^2 + 3x - 8) + (2x^2 - x + 9).$$ 2. To add polynomials, combine like terms. Like terms have the same variable raised to the same power. 3. Group the like terms: $$x^2 + 2x^2 + 3x - x - 8 + 9$$ 4. Simplify each group: $$ (x^2 + 2x^2) + (3x - x) + (-8 + 9)$$ 5. Calculate each sum: $$3x^2 + 2x + 1$$ 6. The equivalent representation of the sum is: $$3x^2 + 2x + 1$$ 7. Using the key for algebra tiles: - $3x^2$ means three positive $x^2$ tiles. - $2x$ means two positive $x$ tiles. - $1$ means one positive 1 tile. This matches the position hint given: three positive $x^2$ tiles, two positive $x$ tiles, and one positive 1 tile. Final answer: $$3x^2 + 2x + 1$$