**Explanation 1**
The logic involves multiplying the two digits on the left side and adding the first number to the product to get the number on the right side.
For example:
1 + 4 = 4 × 1 + 1 = 5
2 + 5 = 5 × 2 + 2 = 12
3 + 6 = 6 × 3 + 3 = 21
Applying this rule to the next pairs:
4 + 7 = 7 × 4 + 4 = 28 + 4 = 32
5 + 8 = 8 × 5 + 5 = 40 + 5 = 45
Thus, the rule is confirmed.
**Explanation 2**
Given:
1 + 4 = 5
2 + 5 = 12
3 + 6 = 21
Take the differences between the numbers on the right side:
12 – 5 = 7
21 – 12 = 9
These differences form an arithmetic progression with a common difference of 2. Following this sequence, the next difference will be 11, so:
21 + 11 = 32 and 4 + 7 = 32
Continuing, the next difference will be 13:
32 + 13 = 45 and 5 + 8 = 45
Both explanations confirm the logic and the results.
