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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 24

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 24
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 24
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 24
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 997²
  2. Use an identity to find 1005²
  3. Use an identity to find 95²
  4. Use an identity to find 104 × 96
  5. Use an identity to find 47 × 48
  6. Use an identity to find 92²
  7. Use an identity to find 1005 × 995
  8. Use an identity to find 53 × 47
  9. Use an identity to find 97²
  10. Use an identity to find 999²

Factorise using identities

Class 9 · Worksheet 4 · set 24
Name:Date:Score:    / 10

Factorise.

  1. x² + 2x + 1
  2. m² − 9
  3. x² + 16x + 64
  4. 16y² − 81
  5. 16m² − 24m + 9
  6. 4m² − 49
  7. a² + 14a + 49
  8. y² + 16y + 64
  9. 25x² − 36
  10. 25m² − 60m + 36

Expand the cube

Class 9 · Worksheet 5 · set 24
Name:Date:Score:    / 8

Expand using (a + b)³.

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