Factorisation Worksheet for Class 8

Factorisation Worksheet for Class 8

Factorisation Worksheet

Class 8 Mathematics

Name: ____________________
Date: _____________________
Roll No.: _________________

Part A: Take Out the Common Factor

Factorise the following expressions:

  1. 6x + 12
  2. 15y + 25
  3. 8a + 16b
  4. 18m + 27n
  5. 14p + 21q
  6. 10x² + 5x
  7. 12ab + 18a
  8. 9x² + 6x
  9. 20mn + 30m
  10. 16a² + 24a

Part B: Factorisation by Grouping

  1. ax + ay + bx + by
  2. 2x + 2y + 3x + 3y
  3. ab + ac + db + dc
  4. mx + my + nx + ny
  5. 3a + 3b + 2a + 2b
  6. px + py + qx + qy
  7. 5x + 10 + 3x + 6
  8. 7a + 14 + 3a + 6
  9. 4x + 8y + 6x + 12y
  10. 9m + 6n + 3m + 2n

Part C: Factorise Using Identities

  1. x² + 6x + 9
  2. x² − 16
  3. a² + 10a + 25
  4. y² − 25
  5. m² + 14m + 49
  6. p² − 36
  7. x² − 10x + 25
  8. a² − 49
  9. y² + 12y + 36
  10. m² − 81

Part D: Factorise Completely

  1. 3x² + 6x
  2. 4a² + 8a + 12
  3. 5x²y + 10xy
  4. 6m²n + 9mn
  5. 8a³ + 12a²
  6. 10x² + 15x + 5
  7. 12p²q + 18pq
  8. 14a²b + 21ab
  9. 9x³ + 6x²
  10. 16m² + 24m + 8

Part E: Word-Based Questions

  1. A rectangle has area (6x + 12). Factorise to find possible dimensions.
  2. A number expression is (15y + 25). Write it in factorised form.
  3. The area of a square is (x² + 10x + 25). Find its side in factorised form.
  4. A garden area is (x² − 16). Express it as a product of factors.
  5. A rectangle has sides represented by (4x + 8). Factorise.

Part F: Challenge Questions

  1. Factorise: (x² + 2xy + y²)
  2. Factorise: (4x² − 25y²)
  3. Factorise: (a² + b² + 2ab)
  4. Factorise: (9x² − 12x + 4)
  5. Factorise: (16m² − 1)

Factorisation Worksheet – Answer Key

Class 8 Mathematics

Part A: Take Out the Common Factor

  1. 6(x + 2)
  2. 5(3y + 5)
  3. 8(a + 2b)
  4. 9(2m + 3n)
  5. 7(2p + 3q)
  6. 5x(2x + 1)
  7. 6a(2b + 3)
  8. 3x(3x + 2)
  9. 10m(n + 3)
  10. 8a(2a + 3)

Part B: Factorisation by Grouping

  1. (a + b)(x + y)
  2. 2(x + y) + 3(x + y) = (x + y)(2 + 3) = 5(x + y)
  3. a(b + c) + d(b + c) = (a + d)(b + c)
  4. m(x + y) + n(x + y) = (m + n)(x + y)
  5. 3(a + b) + 2(a + b) = (a + b)(3 + 2) = 5(a + b)
  6. p(x + y) + q(x + y) = (p + q)(x + y)
  7. 5(x + 2) + 3(x + 2) = (x + 2)(5 + 3) = 8(x + 2)
  8. 7(a + 2) + 3(a + 2) = (a + 2)(7 + 3) = 10(a + 2)
  9. 4(x + 2y) + 6(x + 2y) = (x + 2y)(4 + 6) = 10(x + 2y)
  10. 9m + 3m + 6n + 2n = 12m + 8n = 4(3m + 2n)

Part C: Factorise Using Identities

  1. (x + 3)²
  2. (x − 4)(x + 4)
  3. (a + 5)²
  4. (y − 5)(y + 5)
  5. (m + 7)²
  6. (p − 6)(p + 6)
  7. (x − 5)²
  8. (a − 7)(a + 7)
  9. (y + 6)²
  10. (m − 9)(m + 9)

Part D: Factorise Completely

  1. 3x(x + 2)
  2. 4(a² + 2a + 3)
  3. 5xy(x + 2)
  4. 3mn(2m + 3)
  5. 4a²(2a + 3)
  6. 5(2x² + 3x + 1)
  7. 6pq(2p + 3)
  8. 7ab(2a + 3)
  9. 3x²(3x + 2)
  10. 8(m² + 3m + 1)

Part E: Word-Based Questions

  1. 6(x + 2) → Dimensions: 6 and (x + 2)
  2. 15y + 25 = 5(3y + 5)
  3. x² + 10x + 25 = (x + 5)² → side = (x + 5)
  4. x² − 16 = (x − 4)(x + 4)
  5. 4x + 8 = 4(x + 2)

Part F: Challenge Questions

  1. (x + y)²
  2. (2x − 5y)(2x + 5y)
  3. (a + b)²
  4. (3x − 2)²
  5. (4m − 1)(4m + 1)