1. **State the problem:** We have a rectangle with width $14x$ and height $y$. There are two shaded strips: one at the top with height $x - 8$ and one on the right side with width $x - 8$. We need to find the area of the blank (unshaded) region inside the rectangle. 2. **Understand the problem:** The total area of the rectangle is given by the product of its width and height: $$\text{Total area} = 14x \times y = 14xy$$ 3. **Calculate the area of the shaded strips:** - The top strip has width equal to the full width $14x$ and height $x - 8$, so its area is: $$14x \times (x - 8) = 14x(x - 8) = 14x^2 - 112x$$ - The right strip has height equal to the full height $y$ and width $x - 8$, so its area is: $$y \times (x - 8) = y(x - 8) = xy - 8y$$ 4. **Calculate the overlapping area:** The top strip and right strip overlap in the top-right corner. This overlapping area is a rectangle with width $x - 8$ and height $x - 8$, so its area is: $$(x - 8)(x - 8) = (x - 8)^2 = x^2 - 16x + 64$$ 5. **Calculate the total shaded area:** Add the areas of the two strips and subtract the overlapping area to avoid double counting: $$\text{Shaded area} = (14x^2 - 112x) + (xy - 8y) - (x^2 - 16x + 64)$$ Simplify: $$= 14x^2 - 112x + xy - 8y - x^2 + 16x - 64$$ $$= (14x^2 - x^2) + (-112x + 16x) + xy - 8y - 64$$ $$= 13x^2 - 96x + xy - 8y - 64$$ 6. **Calculate the blank (unshaded) area:** Subtract the shaded area from the total area: $$\text{Blank area} = 14xy - (13x^2 - 96x + xy - 8y - 64)$$ Simplify: $$= 14xy - 13x^2 + 96x - xy + 8y + 64$$ $$= (14xy - xy) - 13x^2 + 96x + 8y + 64$$ $$= 13xy - 13x^2 + 96x + 8y + 64$$ **Final answer:** $$\boxed{13xy - 13x^2 + 96x + 8y + 64}$$