Rectangle Area Comparison: Finding Difference Between (x+4)(x+3) and (x+5)(x+2)

Let's calculate the area of each rectangle step by step:

Step 1: Calculate the area of Rectangle A.
- Dimensions are $(x+4)$ and $(x+3)$.
- The area is calculated as $(x+4) \times (x+3)$.

Expanding this expression using the distributive property, we get:
$(x+4)(x+3) = x \cdot x + x \cdot 3 + 4 \cdot x + 4 \cdot 3$
$\Rightarrow x^2 + 3x + 4x + 12$
$\Rightarrow x^2 + 7x + 12$

Step 2: Calculate the area of Rectangle B.
- Dimensions are $(x+5)$ and $(x+2)$.
- The area is calculated as $(x+5) \times (x+2)$.

Using the distributive property to expand:
$(x+5)(x+2) = x \cdot x + x \cdot 2 + 5 \cdot x + 5 \cdot 2$
$\Rightarrow x^2 + 2x + 5x + 10$
$\Rightarrow x^2 + 7x + 10$

Step 3: Compare the areas of Rectangle A and B.
- Area of Rectangle A: $x^2 + 7x + 12$
- Area of Rectangle B: $x^2 + 7x + 10$

Subtract the area of Rectangle B from the area of Rectangle A:
$(x^2 + 7x + 12) - (x^2 + 7x + 10) = (x^2 + 7x + 12) - x^2 - 7x - 10$
$\Rightarrow x^2 - x^2 + 7x - 7x + 12 - 10$
$\Rightarrow 2$

Thus, the area of Rectangle A is larger by $2$ area units.

The correct answer, therefore, is: The area of rectangle A is larger by 2 area units.