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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 82

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 82
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 82
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 82
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 1009 × 991
  2. Use an identity to find 52 × 48
  3. Use an identity to find 106²
  4. Use an identity to find 49 × 50
  5. Use an identity to find 109 × 91
  6. Use an identity to find 59²
  7. Use an identity to find 1005 × 995
  8. Use an identity to find 106 × 94
  9. Use an identity to find 1004 × 996
  10. Use an identity to find 99²

Factorise using identities

Class 9 · Worksheet 4 · set 82
Name:Date:Score:    / 10

Factorise.

  1. a² − 64
  2. 16y² − 24y + 9
  3. y² + 2y + 1
  4. 25a² − 40a + 16
  5. 16m² − 24m + 9
  6. 9y² − 49
  7. 4y² + 12y + 9
  8. 4x² − 4x + 1
  9. m² + 10m + 25
  10. 25m² + 60m + 36

Expand the cube

Class 9 · Worksheet 5 · set 82
Name:Date:Score:    / 8

Expand using (a + b)³.

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