| d | ( | d | + | 1 | ) | ( | d | + | 3 | ) | + | ( | d | + | 2 | ) | ( | d | + | 1 | ) | d | = | d | ( | d | + | 2 | ) | ( | d | + | 3 | ) | + | ( | d | + | 1 | ) | ( | d | + | 2 | ) | ( | d | + | 3 | ) |
| Left side of the equation = | d | d | ( | d | + | 3 | ) | + | d | × | 1 | ( | d | + | 3 | ) | + | ( | d | + | 2 | ) | ( | d | + | 1 | ) | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 1 | ( | d | + | 3 | ) | + | ( | d | + | 2 | ) | ( | d | + | 1 | ) | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 1 | d | + | d | × | 1 | × | 3 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 1 | d | + | d | × | 3 | + | ( | d | + | 2 | ) |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 1 | d | + | 3 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 1 | d | + | 3 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 1 | d | + | 3 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 1 | d | + | 3 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 1 | d | + | 5 | d | + | d |
| d | d | d | + | d | d | × | 3 | + | d | × | 1 | d | + | 5 | d | + | d | = | d | ( | d | + | 2 | ) | ( | d | + | 3 | ) | + | ( | d | + | 1 | ) | ( | d | + | 2 | ) | ( | d | + | 3 | ) |
| Right side of the equation = | d | d | ( | d | + | 3 | ) | + | d | × | 2 | ( | d | + | 3 | ) | + | ( | d | + | 1 | ) | ( | d | + | 2 | ) | ( | d | + | 3 | ) |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | ( | d | + | 3 | ) | + | ( | d | + | 1 | ) | ( | d | + | 2 | ) | ( | d | + | 3 | ) |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | d | × | 2 | × | 3 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | d | × | 6 | + | ( | d | + | 1 | ) |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 6 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 6 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 6 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 6 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 6 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 12 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 12 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 12 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 12 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 12 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 15 | d | + | d |