Question: A farmer plants a garden that contains corn and pumpkins. The total area (in square feet) of the garden is modeled by the expression $2x^2+5x+4$. The area of the corn is modeled by the expression $x^2-3x+2$. Write an equation in standard form that models the area $A$ of the pumpkins. The equation is $A=$
1. **State the problem:** We are given the total area of the garden as $$2x^2 + 5x + 4$$ and the area of the corn as $$x^2 - 3x + 2$$. We need to find the area of the pumpkins, denoted as $$A$$.
2. **Formula used:** The total area is the sum of the areas of corn and pumpkins. So,
$$\text{Total area} = \text{Area of corn} + \text{Area of pumpkins}$$
which means
$$2x^2 + 5x + 4 = (x^2 - 3x + 2) + A$$
3. **Isolate $$A$$:**
$$A = (2x^2 + 5x + 4) - (x^2 - 3x + 2)$$
4. **Simplify the expression:**
$$A = 2x^2 + 5x + 4 - x^2 + 3x - 2$$
5. **Combine like terms:**
$$A = (2x^2 - x^2) + (5x + 3x) + (4 - 2)$$
$$A = x^2 + 8x + 2$$
6. **Final answer:** The area of the pumpkins in standard form is
$$A = x^2 + 8x + 2$$