Final answer:
The area of the rectangular swimming pool is found by multiplying the length (16x+4) by the width (8x+2). Simplifying, we get the expression 128x² + 64x + 8 square feet. Therefore, the correct answer is option A.
Step-by-step explanation:
The question asks for the expression that represents the area of the bottom of a rectangular swimming pool with given dimensions in terms of 'x'. The length of the pool is provided as 16x+4 feet and the width as 8x+2 feet. To find the area, we use the formula for the area of a rectangle, which is length × width.
Calculating the area, we get:
- (16x + 4) × (8x + 2) = (16x × 8x) + (16x × 2) + (4 × 8x) + (4 × 2).
- 128x² + 32x + 32x + 8
- 128x² + 64x + 8 square feet.
Therefore, the correct expression for the area is 128x² + 64x + 8 square feet, which matches option A.