Squaring and Multiplying Around a Base

Use these tricks when squaring numbers near a round number or multiplying numbers equally spaced from one.

Multiply Numbers Above and Below the Base (Same Distance)

Formula: (base + b)(base − b) = base² − b²

  1. Identify the base and the distance b from it.
  2. Square the base.
  3. Square the distance.
  4. Subtract the two.
102 × 98
Base = 100, b = 2 → 100² − 2²
= 10000 − 4 = 9996

Square Numbers Near a Base

Formula: (base ± b)² = base² ± 2×b×base + b²

  1. Write the number as (base ± b).
  2. Square the base.
  3. Compute ±2×b×base.
  4. Square b.
  5. Add everything together.
47²
Base = 50, b = 3 → 50² − 2×3×50 + 3²
= 2500 − 300 + 9 = 2209
103²
Base = 100, b = 3 → 100² + 2×3×100 + 3²
= 10000 + 600 + 9 = 10609

These calculations would be much more difficult to do if it wasn't for these impressive formulas.