karinalo23
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What is the completely factored form of [tex]\( 12xy - 9x - 8y + 6 \)[/tex]?

A. [tex]\( (3x - 2)(4y - 3) \)[/tex]

B. [tex]\( 3x(4y - 3) - 2(4y + 3) \)[/tex]

C. [tex]\( -6x(4y - 3)(4y - 3) \)[/tex]

D. [tex]\( (3x - 2)(4y - 3)(4y - 3) \)[/tex]

Sagot :

GinnyAnswer
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.
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