Question

17 x 17 using breakdown method

Answer 1

To calculate \( 17 \times 17 \) using the breakdown method, we can break it down into more manageable parts.

1. **Break down 17**:
- \( 17 = 10 + 7 \)

2. **Set up the multiplication**:
- \( 17 \times 17 = (10 + 7) \times (10 + 7) \)

3. **Apply the distributive property (also known as the FOIL method)**:
\[
(10 + 7) \times (10 + 7) = 10 \times 10 + 10 \times 7 + 7 \times 10 + 7 \times 7
\]

4. **Calculate each term**:
- \( 10 \times 10 = 100 \)
- \( 10 \times 7 = 70 \)
- \( 7 \times 10 = 70 \)
- \( 7 \times 7 = 49 \)

5. **Add all the products together**:
\[
100 + 70 + 70 + 49
\]

- First, add the tens: \( 100 + 70 + 70 = 240 \)
- Then, add the last term: \( 240 + 49 = 289 \)

So, \( 17 \times 17 = 289 \).