Kung Fu Math · kungfumath.app
Squares & conjugates
Split a square into smaller areas to see where every term comes from. The middle term appears twice.
Three essential identities
- (a + b)² = a² + 2ab + b²
- (a − b)² = a² − 2ab + b²
- (a + b)(a − b) = a² − b²
Mental calculation
- 23² = (20 + 3)² = 400 + 120 + 9 = 529
- 49² = (50 − 1)² = 2500 − 100 + 1 = 2401
- 48 × 52 = (50 − 2)(50 + 2) = 2500 − 4 = 2496
Reverse the pattern
- x² + 10x + 25 = (x + 5)²
- x² − 16 = (x − 4)(x + 4)
- Do not forget 2ab: (a + b)² is NOT a² + b².
Kung Fu Math · algebra-identities · kungfumath.app/cheat-sheets