Algebraic identities · बीजीय सर्वसमिकाएँ
Learn the 9 identities, then use them for fast sums like 103² and 52 × 48.
Algebraic identities games
Algebraic identities
| (a + b)² | a² + 2ab + b² |
| (a − b)² | a² − 2ab + b² |
| (a + b)(a − b) | a² − b² |
| (x + a)(x + b) | x² + (a + b)x + ab |
| (a + b)³ | a³ + b³ + 3ab(a + b) |
| (a − b)³ | a³ − b³ − 3ab(a − b) |
| a³ + b³ | (a + b)(a² − ab + b²) |
| a³ − b³ | (a − b)(a² + ab + b²) |
| (a + b + c)² | a² + b² + c² + 2ab + 2bc + 2ca |
Identities are true for every value of the letters. Use them for quick sums: 103² = (100 + 3)² = 10000 + 600 + 9 = 10609.
For Class 8 and 9 (NCERT Ganita Manjari 9, “Exploring Algebraic Identities”). Number answers are computed by a program.
A one-page chart to stick on the wall, and a worksheet to practise.
Algebraic identities
| (a + b)² | a² + 2ab + b² |
| (a − b)² | a² − 2ab + b² |
| (a + b)(a − b) | a² − b² |
| (x + a)(x + b) | x² + (a + b)x + ab |
| (a + b)³ | a³ + b³ + 3ab(a + b) |
| (a − b)³ | a³ − b³ − 3ab(a − b) |
| a³ + b³ | (a + b)(a² − ab + b²) |
| a³ − b³ | (a − b)(a² + ab + b²) |
| (a + b + c)² | a² + b² + c² + 2ab + 2bc + 2ca |
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Algebraic identities — worksheet
Name: ____________________ Class: ______ Date: __________
1. Expand: (2x + 3)² = ______ (a − 4)² = ______
2. Find using identities: 101² = ____ 99² = ____ 47 × 53 = ____
3. Factorise: x² − 49 = ______ a³ + 8 = ______
4. Find (x + 3)(x + 5) = ______
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