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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 88

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 88
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 88
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 88
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 46²
  2. Use an identity to find 54 × 55
  3. Use an identity to find 104²
  4. Use an identity to find 49²
  5. Use an identity to find 55 × 45
  6. Use an identity to find 43 × 44
  7. Use an identity to find 993²
  8. Use an identity to find 102²
  9. Use an identity to find 994²
  10. Use an identity to find 1009 × 991

Factorise using identities

Class 9 · Worksheet 4 · set 88
Name:Date:Score:    / 10

Factorise.

  1. 9m² − 30m + 25
  2. 25y² − 64
  3. 25y² − 60y + 36
  4. 25x² + 20x + 4
  5. 4x² − 4x + 1
  6. 9a² − 49
  7. y² − 8y + 16
  8. 16y² − 40y + 25
  9. 16a² − 40a + 25
  10. 25x² + 60x + 36

Expand the cube

Class 9 · Worksheet 5 · set 88
Name:Date:Score:    / 8

Expand using (a + b)³.

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