Mathematics · Class 8
Algebraic Expressions and Identities
Standard identities (a±b)², a²−b², and factorisation using identities.
4 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Master addition, subtraction, multiplication of algebraic expressions and standard identities — (a+b)², (a−b)², a²−b² — for fast factorisation and expansion.
Identities
Identity I
(a + b)² = a² + 2ab + b²
Identity II
(a − b)² = a² − 2ab + b²
Identity III
a² − b² = (a + b)(a − b)
Identity IV
(x + a)(x + b) = x² + (a+b)x + ab
Multiplication
- Monomial × monomial: multiply coefficients and variables
- Monomial × polynomial: distribute
- Polynomial × polynomial: term by term
Applications
Use identities to evaluate 103², 99² mentally and to factorise expressions quickly.
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Expand
Expand (2x + 3)².
- 1(2x)² + 2(2x)(3) + 3²
- 2= 4x² + 12x + 9
Answer
4x² + 12x + 9
Example 2: Using a²−b²
Evaluate 105 × 95.
- 1(100+5)(100−5) = 100² − 5²
- 2= 10000 − 25
Answer
9975
Key Points to Remember
- ✓ Identity holds for all values of variables
- ✓ Middle term sign matters in (a±b)²
- ✓ Factorisation reverses expansion
Exam Tips
- • Identify which identity applies
- • Check middle term: 2ab
Practice MCQs — Algebraic Expressions and Identities
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
(a+b)² equals: