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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 12

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 12
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 12
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 12
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 94²
  2. Use an identity to find 105 × 95
  3. Use an identity to find 107 × 93
  4. Use an identity to find 95 × 96
  5. Use an identity to find 54²
  6. Use an identity to find 996²
  7. Use an identity to find 106 × 94
  8. Use an identity to find 41 × 42
  9. Use an identity to find 58²
  10. Use an identity to find 99 × 100

Factorise using identities

Class 9 · Worksheet 4 · set 12
Name:Date:Score:    / 10

Factorise.

  1. 16x² + 56x + 49
  2. 25a² − 64
  3. m² + 16m + 64
  4. 25m² − 20m + 4
  5. x² + 2x + 1
  6. y² − 1
  7. m² − 18m + 81
  8. 9y² − 48y + 64
  9. 25m² + 80m + 64
  10. 9a² − 25

Expand the cube

Class 9 · Worksheet 5 · set 12
Name:Date:Score:    / 8

Expand using (a + b)³.

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

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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.