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Gyaan Maths
CBSE · Class 6-10
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CBSE Maths · Class 8

Chapter 9: Algebraic Expressions and Identities

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Date: ______________
Marks: ____ / 10

Expansions using identities: (a±b)2(a\pm b)^2, (a+b)(a−b)(a+b)(a-b), (x+a)(x+b)(x+a)(x+b).

Questions

  1. Expand (3x−2y)2(3x-2y)^2.
  2. Evaluate 98298^2 using identity.
  3. (x+2)(x−3)(x+2)(x-3).
  4. (x+3)(x+5)(x + 3)(x + 5).
  5. (2a−3b)2(2a - 3b)^2.
  6. (102)2(102)^2.
  7. 103×97103 \times 97.
  8. (a+2b)3(a + 2b)^3.
  9. (x−4)(x+4)(x - 4)(x + 4).
  10. (a+b+c)2(a+b+c)^2 expansion.

Extra Practice (Optional)

  • Expand (2p−3q)(2p+3q)(2p-3q)(2p+3q).
  • Evaluate 103×97103\times 97.
  • (5x−1)2(5x-1)^2.

Answer Key (For Teachers)

  1. Answer: 9x2−12xy+4y29x^2-12xy+4y^2.
    Working: 9x2−12xy+4y29x^2 - 12xy + 4y^2.
  2. Answer: 96049604.
    Working: (100−2)2(100-2)^2.
  3. Answer: x2−x−6x^2 - x - 6.
    Working: x2−x−6x^2 - x - 6.
  4. Answer: x2+8x+15x^2 + 8x + 15
    Working: (x+a)(x+b)(x+a)(x+b) identity.
  5. Answer: 4a2−12ab+9b24a^2 - 12ab + 9b^2
    Working: (a−b)2(a-b)^2 pattern.
  6. Answer: 1040410404
    Working: (100+2)2(100+2)^2.
  7. Answer: 99919991
    Working: (a+b)(a−b)(a+b)(a-b).
  8. Answer: a3+6a2b+12ab2+8b3a^3 + 6a^2b + 12ab^2 + 8b^3
    Working: Cube identity.
  9. Answer: x2−16x^2 - 16
    Working: a2−b2a^2-b^2.
  10. Answer: a2+b2+c2+2(ab+bc+ca)a^2+b^2+c^2+2(ab+bc+ca)
    Working: Formula.
Gyaan Maths · CBSE Class 8 · Chapter 9
Gyaan Maths — CBSE Class 6-10, built for board-toppers.
v1.1 · Feb 2026