To factor out the greatest common factor (GCF) of the expression [tex]\( 9 - 12x + 6y \)[/tex], we follow these steps:
1. Identify the GCF:
- The terms in the expression are [tex]\(9\)[/tex], [tex]\(-12x\)[/tex], and [tex]\(6y\)[/tex].
- The numerical coefficients are [tex]\(9\)[/tex], [tex]\(-12\)[/tex], and [tex]\(6\)[/tex].
- First, determine the GCF of these numerical coefficients:
- The prime factors of [tex]\(9\)[/tex] are [tex]\(3 \times 3\)[/tex].
- The prime factors of [tex]\(-12\)[/tex] are [tex]\(-1 \times 2 \times 2 \times 3\)[/tex].
- The prime factors of [tex]\(6\)[/tex] are [tex]\(2 \times 3\)[/tex].
- The common factor among the numerical coefficients is [tex]\(3\)[/tex].
2. Factor out the GCF:
- Since the GCF of the coefficients is [tex]\(3\)[/tex], we factor [tex]\(3\)[/tex] out of each term in the expression:
[tex]\[
9 \div 3 = 3
\][/tex]
[tex]\[
-12x \div 3 = -4x
\][/tex]
[tex]\[
6y \div 3 = 2y
\][/tex]
3. Rewrite the expression:
- Factor [tex]\(3\)[/tex] out of the entire expression:
[tex]\[
9 - 12x + 6y = 3 \times 3 - 3 \times 4x + 3 \times 2y
\][/tex]
4. Simplify:
- Combine terms within the parentheses to get the final factored form:
[tex]\[
9 - 12x + 6y = 3(3 - 4x + 2y)
\][/tex]
Therefore, the expression [tex]\( 9 - 12x + 6y \)[/tex] factored by applying the distributive property and factoring out the greatest common factor is:
[tex]\[
3(3 - 4x + 2y)
\][/tex]
