The factor form `4(3a-2b)^(2)-5(3a-2b)` is

Options

A. `(3a-2b)[12a-8b-5]`
B. `(2a-3b)[12a-8b-5]`
C. `(3a-2b)[8a-12b-5]`
D. `(3a-2b)[5a-8b-12]`

Answer

To factor the expression \( 4(3a - 2b)^2 - 5(3a - 2b) \), we can follow these steps:

### Step 1: Identify the common factor
The expression has a common factor of \( (3a - 2b) \).

### Step 2: Factor out the common term
We can factor out \( (3a - 2b) \) from both terms:

\[ 4(3a - 2b)^2 - 5(3a - 2b) = (3a - 2b) \left[ 4(3a - 2b) - 5 \right] \]

### Step 3: Simplify the expression inside the brackets
Now, we simplify the expression inside the brackets:

\[ 4(3a - 2b) - 5 \]

Distributing \( 4 \):

\[ = 12a - 8b - 5 \]

### Step 4: Write the final factored form
Now we can write the expression in its factored form:

\[ = (3a - 2b)(12a - 8b - 5) \]

### Final Answer:
Thus, the factor form of the expression \( 4(3a - 2b)^2 - 5(3a - 2b) \) is:

\[ (3a - 2b)(12a - 8b - 5) \]

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