Answer:

factored form of the expression is:

2x(6 + 4c - 4a) + (6 - 4a - 4c)

Step-by-step explanation:

To factor the expression 6(2x+1) + 4a(1-2x) + 4c(2x-1), you can factor it by grouping like terms. Here's the step-by-step solution:

Step 1: Group the terms with common factors.

Group the terms with "2x" and the terms without "2x":

(6(2x+1) - 4a(2x) + 4c(2x)) + (6 - 4a - 4c)

Step 2: Factor out the common factors from each group.

In the first group, factor out 2x:

2x(6 + 4c - 4a) + (6 - 4a - 4c)

Step 3: Simplify the expression.

Now, you have factored the expression:

2x(6 + 4c - 4a) + (6 - 4a - 4c)

So, the factored form of the expression is:

2x(6 + 4c - 4a) + (6 - 4a - 4c)