`8(3a-2b)^2-10(3a-2b)`

Answer

To factor the polynomial \( 8(3a-2b)^2 - 10(3a-2b) \), we will follow these steps:

### Step 1: Identify the common factor
First, we can see that both terms in the expression share a common factor of \( (3a - 2b) \).

### Step 2: Factor out the common term
We will factor out \( (3a - 2b) \) from the expression:
\[ 8(3a-2b)^2 - 10(3a-2b) = (3a - 2b)(8(3a - 2b) - 10) \]

### Step 3: Simplify the expression inside the parentheses
Now, we simplify the expression inside the parentheses:
\[ 8(3a - 2b) - 10 \]
Distributing \( 8 \):
\[ = 24a - 16b - 10 \]

### Step 4: Write the final factored form
Now we can write the complete factored form of the polynomial:
\[ = (3a - 2b)(24a - 16b - 10) \]

### Step 5: Further factor if possible
We can check if the second factor \( 24a - 16b - 10 \) can be factored further. Notice that we can factor out a \( 2 \):
\[ = (3a - 2b)(2(12a - 8b - 5)) \]
So the final factored form is:
\[ = 2(3a - 2b)(12a - 8b - 5) \]

### Final Answer:
The factorized form of the polynomial \( 8(3a-2b)^2 - 10(3a-2b) \) is:
\[ 2(3a - 2b)(12a - 8b - 5) \]

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