Calculate the volume of a trapezoidal prism where b1=3p-6, b2=2p+5, h=4p-8, and a height of 18 cm

1. Calculate the sum of base lengths:

b_1 + b_2 = (3p - 6) + (2p + 5) = 5p - 1

2. Substitute the values into the volume formula:

V = \frac{1}{2} \times (5p - 1) \times (4p - 8) \times 18

3. Multiply by the constant terms:

V = \frac{1}{2} \times (5p - 1) \times (4p - 8) \times 18 = 9 \times (5p - 1) \times (4p - 8)

4. Use the distributive property to expand:

V = 9 \times (20p^2 - 40p - 4p + 8) = 9 \times (20p^2 - 44p + 8)

5. Distribute the 9:

V = 180p^2 - 396p + 72

So, the volume of the trapezoidal prism is:

V = 180p^2 - 396p + 72 \text{ cubic cm}