Certainly! Let's factor the expression [tex]\(7abc + 21bc\)[/tex] using the Greatest Common Factor (GCF). Follow these steps:
1. Identify the Common Factors:
First, we need to find the common factors in each term of the expression [tex]\(7abc + 21bc\)[/tex].
- Both terms have the variable [tex]\(b\)[/tex].
- Both terms have the variable [tex]\(c\)[/tex].
- The coefficients are 7 and 21, where the GCF of 7 and 21 is 7.
2. Factor Out the GCF:
Now we factor out [tex]\(7bc\)[/tex] which is the GCF from both terms.
- For the first term [tex]\(7abc\)[/tex], when we factor out [tex]\(7bc\)[/tex], we are left with [tex]\(a\)[/tex].
- For the second term [tex]\(21bc\)[/tex], when we factor out [tex]\(7bc\)[/tex], we are left with [tex]\(3\)[/tex].
3. Write the Factored Form:
After factoring out [tex]\(7bc\)[/tex], the expression inside the parentheses will contain what remains of each term.
[tex]\[ 7abc + 21bc = 7bc(a + 3) \][/tex]
Thus, the factored form of the expression [tex]\(7abc + 21bc\)[/tex] is:
[tex]\[ \boxed{7bc(a + 3)} \][/tex]
