Final answer:
The expression for the area of the rectangular swimming pool in expanded form, accounting for a path of uniform width x meters around it, is 150 - 50x + 4x² square meters.
Step-by-step explanation:
To find an expression for the area of the swimming pool, we first need to establish the dimensions of the pool itself. The total length of the path and pool together is 15 meters, and the total width is 10 meters. Because the path surrounds the pool and is of uniform width x meters, the length and width of the pool will be reduced by twice the width of the path (subtracting x from each side of the rectangle).
The length of the pool is thus (15 - 2x) meters, and the width of the pool is (10 - 2x) meters. The area of the pool is calculated by multiplying the length by the width, so:
Area of the pool = (15 - 2x) * (10 - 2x)
In expanded form, this becomes:
Area of the pool = 150 - 30x - 20x + 4x²
Combining like terms:
Area of the pool = 150 - 50x + 4x²
This formula gives us the area of the pool in square meters, depending on the width x of the path surrounding it.