1. **State the problem:** Multiply 25824 by 89 step by step. 2. **Formula used:** Multiplication of two numbers can be done using the distributive property: $$a \times b = a \times (b_1 \times 10 + b_0) = a \times b_1 \times 10 + a \times b_0$$ where $b_1$ and $b_0$ are digits of $b$. 3. **Break down 89:** 89 can be written as $80 + 9$. 4. **Multiply 25824 by 9:** $$25824 \times 9 = 232416$$ 5. **Multiply 25824 by 80:** $$25824 \times 80 = 25824 \times (8 \times 10) = (25824 \times 8) \times 10$$ Calculate $25824 \times 8$: $$25824 \times 8 = 206592$$ Then multiply by 10: $$206592 \times 10 = 2065920$$ 6. **Add the two products:** $$232416 + 2065920 = 2298336$$ 7. **Final answer:** $$25824 \times 89 = 2298336$$