1. **State the problem:** Simplify the expression $3 \cdot 1 \cdot b + b ( 2 t^2 + 3 b^2 )$. 2. **Write the expression clearly:** $$3 \times 1 \times b + b ( 2 t^2 + 3 b^2 )$$ 3. **Simplify the multiplication:** Since $3 \times 1 = 3$, the expression becomes: $$3b + b ( 2 t^2 + 3 b^2 )$$ 4. **Distribute $b$ over the terms inside the parentheses:** $$3b + b \cdot 2 t^2 + b \cdot 3 b^2 = 3b + 2 b t^2 + 3 b^3$$ 5. **Write the simplified expression:** $$3b + 2 b t^2 + 3 b^3$$ This is the fully simplified form; no like terms can be combined further because they have different powers or variables. **Final answer:** $$3b + 2 b t^2 + 3 b^3$$