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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 16

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 16
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 16
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 16
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 103²
  2. Use an identity to find 106 × 94
  3. Use an identity to find 109 × 110
  4. Use an identity to find 91 × 92
  5. Use an identity to find 52 × 48
  6. Use an identity to find 57 × 43
  7. Use an identity to find 1004²
  8. Use an identity to find 99 × 100
  9. Use an identity to find 49 × 50
  10. Use an identity to find 47 × 48

Factorise using identities

Class 9 · Worksheet 4 · set 16
Name:Date:Score:    / 10

Factorise.

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

Expand the cube

Class 9 · Worksheet 5 · set 16
Name:Date:Score:    / 8

Expand using (a + b)³.

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