1. Let's analyze the first expression (a): $4a^2 + 12ab$. 2. Factor out the greatest common factor (GCF) from both terms. The GCF of $4a^2$ and $12ab$ is $4a$. 3. After factoring out $4a$, write the remaining terms inside parentheses: $$4a(a + 3b)$$ 4. For the second expression (b): $3pr + 6qr - 2pt - 4qt$ 5. Group terms: $$(3pr + 6qr) - (2pt + 4qt)$$ 6. Factor out the GCF from each group: $$3r(p + 2q) - 2t(p + 2q)$$ 7. Now, factor out the common binomial factor $(p + 2q)$: $$(3r - 2t)(p + 2q)$$ Final answers: (a) $4a(a + 3b)$ (b) $(3r - 2t)(p + 2q)$