The big picture
One rule, eight uses. The number outside reaches every term inside.
| Idea | Remember | Example |
|---|---|---|
| A free cut | A cut never changes the total | 160 + 40 = 200 |
| Over a sum | The outside number meets every term | 8 × (20+5) = 160 + 40 |
| With a letter | Letter or not, the same move | 3(n+4) = 3n + 12 |
| Over a subtraction | Each term keeps its own sign | 7 × (30−2) = 210 − 14 |
| Two brackets | Every term meets every term | (x+2)(x+3) = x² + 5x + 6 |
| Collecting | Only matching letter parts join | 3x + 2x = 5x |
| Squaring a sum | A middle term, twice | (3+4)² = 9 + 24 + 16 |
| A chosen cut | Cut at a round number | 23 × 7 = 140 + 21 |
Part I, Chapter 6 is We Distribute, Yet Things Multiply. Your book also squares a difference. It also multiplies a sum by a difference.