To write the expression [tex]\(4u^2(a - 3) + q(a - 3)\)[/tex] in complete factored form, follow these steps:
1. Identify the common factor in both terms of the expression. Here, both terms [tex]\(4u^2(a - 3)\)[/tex] and [tex]\(q(a - 3)\)[/tex] share a common factor of [tex]\((a - 3)\)[/tex].
2. Factor out [tex]\((a - 3)\)[/tex] from both terms:
[tex]\[
4u^2(a - 3) + q(a - 3) = (a - 3)(4u^2) + (a - 3)q
\][/tex]
3. Combine the remaining terms inside the parentheses:
[tex]\[
(a - 3)(4u^2 + q)
\][/tex]
Therefore, the completely factored form of the expression [tex]\(4u^2(a - 3) + q(a - 3)\)[/tex] is:
[tex]\[
\boxed{(a - 3)(q + 4u^2)}
\][/tex]
