Let's work through the factorization of each expression step-by-step.
### Part (a): Factorize [tex]\(6a + 9ab\)[/tex]
1. Identify the common factors:
Both terms in the expression [tex]\(6a\)[/tex] and [tex]\(9ab\)[/tex] have a common factor of [tex]\(3a\)[/tex].
2. Factor out the common factor [tex]\(3a\)[/tex]:
- [tex]\(6a \div 3a = 2\)[/tex]
- [tex]\(9ab \div 3a = 3b\)[/tex]
3. Rewrite the expression using the factored form:
[tex]\[
6a + 9ab = 3a(2 + 3b)
\][/tex]
Thus, the factorized form of [tex]\(6a + 9ab\)[/tex] is:
[tex]\[
\boxed{3a(2 + 3b)}
\][/tex]
### Part (b): Factorize [tex]\(32xy - 12x^2z\)[/tex]
1. Identify the common factors:
Both terms in the expression [tex]\(32xy\)[/tex] and [tex]\(12x^2z\)[/tex] have a common factor of [tex]\(4x\)[/tex].
2. Factor out the common factor [tex]\(4x\)[/tex]:
- [tex]\(32xy \div 4x = 8y\)[/tex]
- [tex]\(12x^2z \div 4x = 3xz\)[/tex]
3. Rewrite the expression using the factored form:
[tex]\[
32xy - 12x^2z = 4x(8y - 3xz)
\][/tex]
Thus, the factorized form of [tex]\(32xy - 12x^2z\)[/tex] is:
[tex]\[
\boxed{4x(8y - 3xz)}
\][/tex]
These factorized expressions are the solutions to the given problems.
