Tamil Nadu Class 8 Maths Algebra — Samacheer Kalvi

Quick Summary

The Algebra chapter in Class 8 builds on basic expressions to introduce powerful algebraic identities and factorisation techniques. These skills are the foundation for higher algebra in Classes 9 and 10 and carry significant marks in all term exams.

Key Definitions

• Algebraic Expression: A combination of variables, constants, and operations. Example: 3x² + 5x − 7.
• Polynomial: An algebraic expression where powers of variables are non-negative integers.
• Identity: An equation true for all values of the variables.
• Factorisation: Writing an expression as a product of simpler expressions.

Important Algebraic Identities

Using the Identities — Worked Examples

(a + b)²

Expand (2x + 3)²: = (2x)² + 2(2x)(3) + (3)² = 4x² + 12x + 9

(a − b)²

Expand (5m − 2)²: = (5m)² − 2(5m)(2) + (2)² = 25m² − 20m + 4

(a + b)(a − b)

Expand (y + 7)(y − 7): = y² − 49

Using identities for arithmetic:

• 103² = (100 + 3)² = 10000 + 600 + 9 = 10609
• 98 × 102 = (100 − 2)(100 + 2) = 10000 − 4 = 9996

Factorisation

Method 1 — Common Factor

6x² + 9x = 3x(2x + 3)

Method 2 — Grouping

ax + ay + bx + by = a(x + y) + b(x + y) = (a + b)(x + y)

Method 3 — Using Identities

x² + 10x + 25 = (x + 5)² m² − 16 = (m + 4)(m − 4)

Important Questions

One Mark

• Expand (a + 4)² using an identity.
• Factorise: x² − 9.
• Write the identity for (a − b)².
• Evaluate 99² using the identity (100 − 1)².
• Find the product (x + 5)(x − 5).

Short Answer (3 marks)

• Expand and simplify: (3x + 2)² − (3x − 2)².
• Factorise: 4a² − 12ab + 9b².
• Using identity, find the value of 97 × 103.

Long Answer (5 marks)

• Factorise completely: 2x³ + 4x² − 6x, showing each step.
• Expand (2a + 3b)² and (2a − 3b)² and find their sum and difference. Interpret the result using identities.

Common Mistakes

• Forgetting the middle term (2ab) when expanding (a ± b)².
• Applying (a + b)² = a² + b² (wrong — the 2ab term is omitted).
• Not checking if the answer can be further simplified after factorisation.

Revision Checklist

• [ ] I have memorised all four standard identities.
• [ ] I can expand expressions using identities without a calculator.
• [ ] I can factorise by common factor, grouping, and identities.
• [ ] I have used identities to solve numerical problems (e.g., 103²).
• [ ] I have solved all textbook exercises and corrected mistakes.