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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 2

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 2
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

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

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 2
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 1003²
  2. Use an identity to find 1001 × 999
  3. Use an identity to find 52²
  4. Use an identity to find 94 × 95
  5. Use an identity to find 54²
  6. Use an identity to find 1009²
  7. Use an identity to find 46²
  8. Use an identity to find 107 × 93
  9. Use an identity to find 104 × 105
  10. Use an identity to find 59 × 41

Factorise using identities

Class 9 · Worksheet 4 · set 2
Name:Date:Score:    / 10

Factorise.

  1. 9x² − 4
  2. m² − 16m + 64
  3. m² − 6m + 9
  4. 16a² − 9
  5. 9y² − 1
  6. 9m² − 1
  7. a² − 9
  8. m² − 49
  9. m² − 2m + 1
  10. 25y² − 70y + 49

Expand the cube

Class 9 · Worksheet 5 · set 2
Name:Date:Score:    / 8

Expand using (a + b)³.

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

How do I get different questions?

Press “🔄 New set” — the questions change (maths numbers are new every time; English sentences are shuffled).

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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.