`2a^3+16b^3-5a-10b`

Answer

To factor the polynomial \(2a^3 + 16b^3 - 5a - 10b\), we will follow these steps:

### Step 1: Group the terms
We can group the terms in pairs:
\[ (2a^3 + 16b^3) + (-5a - 10b) \]

### Step 2: Factor out the common factors
From the first group \(2a^3 + 16b^3\), we can factor out a 2:
\[ 2(a^3 + 8b^3) \]
From the second group \(-5a - 10b\), we can factor out \(-5\):
\[ -5(a + 2b) \]
So, we rewrite the expression as:
\[ 2(a^3 + 8b^3) - 5(a + 2b) \]

### Step 3: Recognize the sum of cubes
The term \(a^3 + 8b^3\) can be factored using the sum of cubes formula:
\[ x^3 + y^3 = (x + y)(x^2 - xy + y^2) \]
Here, \(x = a\) and \(y = 2b\). Thus:
\[ a^3 + (2b)^3 = (a + 2b)(a^2 - 2ab + 4b^2) \]

### Step 4: Substitute back into the expression
Substituting this back into our expression, we have:
\[ 2((a + 2b)(a^2 - 2ab + 4b^2)) - 5(a + 2b) \]

### Step 5: Factor out the common binomial factor
Now, we can see that \((a + 2b)\) is a common factor:
\[ (a + 2b)(2(a^2 - 2ab + 4b^2) - 5) \]

### Step 6: Final expression
Thus, the factored form of the polynomial \(2a^3 + 16b^3 - 5a - 10b\) is:
\[ (a + 2b)(2a^2 - 4ab + 8b^2 - 5) \]