ID001 · Algebraic identities · Classes 8–10
(a + b)²
The square of a sum: a square of side a + b splits into a², two ab rectangles and b².
(a+b)²(a + b)²
📐 Formula
(a + b)² = a² + 2ab + b²
✏️ Worked example
(3 + 1)² = 9 + 6 + 1 = 16.
🌍 Where it is used
Fast squaring: 21² = (20 + 1)² = 400 + 40 + 1 = 441.
❓ Quick check
(x + 5)² = ?
🏋️ Practice
Easy(x + 1)² = ?
Answer: x² + 2x + 1
MediumFind 51² using the identity.
Answer: 2500 + 100 + 1 = 2601
Challenge(2a + 3b)² = ?
Answer: 4a² + 12ab + 9b²