The product of the given expressions is 10x^3 - 83x^2 + 150x - 72.
To find the product (2x-3)(6-x)(4-5x), we can use the distributive property and multiply the expressions together. Let's break down the steps:
Step 1: Multiply the first two expressions, (2x-3) and (6-x), using the distributive property:
(2x-3)(6-x) = 2x(6-x) - 3(6-x)
= 12x - 2x^2 - 18 + 3x
= -2x^2 + 15x - 18
Step 2: Multiply the result from step 1, (-2x^2 + 15x - 18), by the third expression (4-5x), again using the distributive property:
(-2x^2 + 15x - 18)(4-5x) = -2x^2(4-5x) + 15x(4-5x) - 18(4-5x)
= -8x^2 + 10x^3 + 60x - 75x^2 - 72 + 90x
= 10x^3 - 83x^2 + 150x - 72
Therefore, the product of (2x-3)(6-x)(4-5x) is 10x^3 - 83x^2 + 150x - 72.