To find the completely factored form of the expression 12xy + 9x + 8y + 6, we first need to group the terms.
Start by rearranging the expression for easier factoring:
- (12xy + 9x) + (8y + 6)
Now, we can factor out the common terms in each group:
- From the first group, 12xy + 9x, we can factor out 3x:
3x(4y + 3) - From the second group, 8y + 6, we can factor out 2:
2(4y + 3)
This gives us:
- 3x(4y + 3) + 2(4y + 3)
Now we can see that (4y + 3) is a common factor in both terms:
- Factoring out (4y + 3) gives us:
- (4y + 3)(3x + 2)
Hence, the completely factored form of the expression 12xy + 9x + 8y + 6 is:
(4y + 3)(3x + 2).