1. The problem asks to express the area of rectangles formed by tiles as a product of length and as a sum of parts. 2. For part (a), the rectangle has dimensions $(x + 3)$ and $(x^2 + x)$. 3. The product form of the area is simply the multiplication of these two expressions: $$\text{Area} = (x + 3)(x^2 + x)$$ 4. To write the area as a sum of parts, we consider the smaller rectangles formed: - Left rectangle area: $x \times x = x^2$ - Right rectangle area: $3 \times x = 3x$ 5. Adding these parts gives the sum form: $$\text{Area} = x^2 + 3x$$ 6. For part (b), the rectangle has dimensions $(x + 1)$ and $(x^2 + 2x + 2)$. 7. The product form of the area is: $$\text{Area} = (x + 1)(x^2 + 2x + 2)$$ 8. The sum form comes from the three smaller rectangles: - Leftmost rectangle: $x \times x = x^2$ - Middle rectangle: $2 \times x = 2x$ - Rightmost rectangle: $1 \times x = x$ 9. Adding these parts gives: $$\text{Area} = x^2 + 2x + x = x^2 + 3x$$ 10. Note: The problem states the height as $x^2 + 2x + 2$ but the sum of parts only accounts for $x^2 + 3x$. This suggests the sum of parts corresponds to the tiled areas, while the product form is the full expression. Final answers: - (a) Product: $(x + 3)(x^2 + x)$, Sum: $x^2 + 3x$ - (b) Product: $(x + 1)(x^2 + 2x + 2)$, Sum: $x^2 + 3x$