Solve using short cut methods: `74xx25`

Answer

To solve the multiplication of \( 74 \times 25 \) using shortcut methods, we can break it down into simpler steps. Here’s how we can do it:

### Step-by-Step Solution:

1. **Break Down the Numbers**:
We can express \( 74 \) as \( 70 + 4 \).
\[ 74 = 70 + 4 \]

2. **Distribute the Multiplication**:
Now, we can distribute \( 25 \) to both \( 70 \) and \( 4 \).
\[ 74 \times 25 = (70 + 4) \times 25 = 70 \times 25 + 4 \times 25 \]

3. **Calculate Each Part**:
- First, calculate \( 70 \times 25 \):
\[ 70 \times 25 = 1750 \]
- Next, calculate \( 4 \times 25 \):
\[ 4 \times 25 = 100 \]

4. **Add the Results Together**:
Now, we add the two results:
\[ 1750 + 100 = 1850 \]

5. **Final Answer**:
Therefore, the product of \( 74 \times 25 \) is:
\[ \boxed{1850} \]