(3u-4x-6)(u+2x)

1. Distribute each term in the first bracket by each term in the second bracket:

(3u)(u) = 3u^2
(3u)(2x) = 6ux
(-4x)(u) = -4xu
(-4x)(2x) = -8x^2
(-6)(u) = -6u
(-6)(2x) = -12x

2. Combine like terms:

3u^2 + 6ux - 4xu - 8x^2 - 6u - 12x

Use the fact that \(6ux\) and \(-4xu\) are like terms:

6ux - 4xu = 2ux

Therefore, the final expression is

3u^2 + 2ux - 8x^2 - 6u - 12x

Answer:

3u^2 + 2ux - 8x^2 - 6u - 12x