To express the given expression [tex]\(60ab - 72b\)[/tex] as a product using the greatest common factor (GCF), we need to follow these steps:
1. Identify the terms:
The expression consists of two terms: [tex]\(60ab\)[/tex] and [tex]\(72b\)[/tex].
2. Find the GCF of the terms:
- The term [tex]\(60ab\)[/tex] can be factored into its prime components along with variables: [tex]\(60ab = 2 \times 2 \times 3 \times 5 \times a \times b\)[/tex].
- The term [tex]\(72b\)[/tex] can be factored into its prime components along with the variable: [tex]\(72b = 2 \times 2 \times 2 \times 3 \times 3 \times b\)[/tex].
- The common factors between the two terms are [tex]\(2 \times 2 \times 3 \times b = 12b\)[/tex].
3. Factor out the GCF from each term:
- Dividing [tex]\(60ab\)[/tex] by [tex]\(12b\)[/tex], we get [tex]\( \frac{60ab}{12b} = 5a\)[/tex].
- Dividing [tex]\(72b\)[/tex] by [tex]\(12b\)[/tex], we get [tex]\( \frac{72b}{12b} = 6\)[/tex].
4. Write the expression as a product:
- After factoring out the GCF, the expression becomes [tex]\(12b(5a - 6)\)[/tex].
Thus, the correct choice showing the expression factored as a product is:
[tex]\[ 12b(5a - 6) \][/tex]
This matches the second option:
[tex]\[ 12b(5a - 6) \][/tex]
