Chapter 12 · ICSE Class 8 Mathematics

Algebraic Identities

Learn the three core algebraic identities that let you expand and simplify expressions instantly, without multiplying term by term.

🧮 Chapter 12

The expansion of (a minus b) squared shown as a square with a smaller square removed A square of side a with a smaller square of side b cut from one corner, illustrating why (a-b) squared equals a squared minus 2ab plus b squared a b (a−b)² = a²−2ab+b²
12.1

Square Identities

Two key identities: (a+b)² = a² + 2ab + b², and (a−b)² = a² − 2ab + b². These let you expand a squared binomial instantly instead of multiplying it out.

1

Expand (x + 5)² using the identity.

x² + 2(x)(5) + 5² = x² + 10x + 25

2

Expand (2y − 3)² using the identity.

(2y)² − 2(2y)(3) + 3² = 4y² − 12y + 9

12.2

Difference of Squares

The identity a² − b² = (a+b)(a−b) lets you factor or expand expressions involving the difference of two squares instantly.

1

Expand (x + 4)(x − 4) using the identity.

x² − 4² = x² − 16

2

Use the identity to find 52 × 48 (Hint: think of it as (50+2)(50−2)).

50² − 2² = 2500 − 4 = 2496

Practice

Exercises

1. Expand (x + 7)² using the identity.

2. Expand (3a − 2b)² using the identity.

3. Expand (y + 6)(y − 6) using the identity.

4. Use the identity a² − b² = (a+b)(a−b) to find 105 × 95.

5. Expand (2x + 5)² using the identity.

🎉 Great work! You've completed all the Class 8 chapters built so far. More coming soon! ← Back to the full map