To find the completely factored form of the expression [tex]\(12xy - 9x - 8y + 6\)[/tex], we need to follow a step-by-step factorization process. Here is the detailed solution:
1. Group the terms:
We start by grouping the terms in a way that makes it easier to factor by grouping.
[tex]\[
(12xy - 9x) + (-8y + 6)
\][/tex]
2. Factor out the common factors from each group:
- In the first group [tex]\(12xy - 9x\)[/tex], both terms have a common factor of [tex]\(3x\)[/tex].
- In the second group [tex]\(-8y + 6\)[/tex], both terms have a common factor of [tex]\(-2\)[/tex].
So, we factor out these common factors:
[tex]\[
3x(4y - 3) - 2(4y - 3)
\][/tex]
3. Factor out the common binomial:
Notice that [tex]\((4y - 3)\)[/tex] is common in both terms:
[tex]\[
(3x - 2)(4y - 3)
\][/tex]
Thus, the expression [tex]\(12xy - 9x - 8y + 6\)[/tex] factors completely to:
[tex]\[
(3x - 2)(4y - 3)
\][/tex]
This is the completely factored form of the given expression.
