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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 6

Algebra formulas sheet — identities, with practice questions

Free algebra formulas sheet: (a + b)², (a − b)², (a + b)(a − b), (a + b)³ and more, with printable practice — expand, factorise and use identities to calculate, with answers.

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Expand the square (Class 8–9)(a + b)(a − b) (Class 8–9)Calculate with identities (Class 8–9)Factorise using identities (Class 9)Expand the cube (Class 9)

Expand the square

Class 8–9 · Worksheet 1 · set 6
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 6
Name:Date:Score:    / 10

Multiply using (a + b)(a − b) = a² − b².

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 6
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 999²
  2. Use an identity to find 45 × 46
  3. Use an identity to find 103 × 97
  4. Use an identity to find 994²
  5. Use an identity to find 1009 × 991
  6. Use an identity to find 1008²
  7. Use an identity to find 51 × 52
  8. Use an identity to find 1007 × 993
  9. Use an identity to find 92 × 93
  10. Use an identity to find 98²

Factorise using identities

Class 9 · Worksheet 4 · set 6
Name:Date:Score:    / 10

Factorise.

  1. 9m² + 6m + 1
  2. 4y² − 4y + 1
  3. 25a² + 80a + 64
  4. a² − 16
  5. 25y² + 90y + 81
  6. 9m² − 25
  7. 9y² − 42y + 49
  8. 16a² + 56a + 49
  9. 4m² + 20m + 25
  10. 25a² − 16

Expand the cube

Class 9 · Worksheet 5 · set 6
Name:Date:Score:    / 8

Expand using (a + b)³.

  1. (x + 2)³
  2. (x + 1)³
  3. (x + 5)³
  4. (x + 3)³
  5. (x − 5)³
  6. (x + 4)³
  7. (x − 3)³
  8. (x − 2)³

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Questions

What are the basic algebraic identities?

(a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b² and (a + b)(a − b) = a² − b² — learn these three first; the others build on them.

Are these worksheets free?

Yes — print them or save as PDF free. Every worksheet has an answer key.

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Can my child do this worksheet online, like a quiz?

Yes — press “▶️ Practise online” on any worksheet. The questions come one at a time with instant marking, a score at the end and a review of mistakes. No sign-in is needed.