Subjects algebra

Rectangle Area 145Bc9

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1. **State the problem:** We need to find the area of the entire large rectangle, which is divided into three smaller rectangles horizontally. 2. **Identify dimensions:** The height of the entire rectangle is given as $5m^4$. 3. **Width of the entire rectangle:** The width is the sum of the widths of the three smaller rectangles. The right rectangle's width is given as $m^2 - 2m - 1$ (rewriting $m^2 + -2m + -1$ in standard form). The widths of the other two rectangles are not explicitly given, so we assume the total width is $m^2 - 2m - 1$. 4. **Formula for area of a rectangle:** $$\text{Area} = \text{height} \times \text{width}$$ 5. **Calculate the area:** $$\text{Area} = 5m^4 \times (m^2 - 2m - 1)$$ 6. **Distribute multiplication:** $$= 5m^4 \times m^2 - 5m^4 \times 2m - 5m^4 \times 1$$ $$= 5m^{6} - 10m^{5} - 5m^{4}$$ 7. **Final answer:** The area of the entire rectangle expressed as a polynomial in standard form is: $$\boxed{5m^{6} - 10m^{5} - 5m^{4}}$$