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

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
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

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

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

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

Calculate with identities

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

Use an identity — no long multiplication.

  1. Use an identity to find 97 × 98
  2. Use an identity to find 45 × 46
  3. Use an identity to find 107 × 108
  4. Use an identity to find 48 × 49
  5. Use an identity to find 57 × 43
  6. Use an identity to find 102 × 98
  7. Use an identity to find 104²
  8. Use an identity to find 94²
  9. Use an identity to find 103 × 97
  10. Use an identity to find 1008 × 992

Factorise using identities

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

Factorise.

  1. 9y² + 6y + 1
  2. 25a² − 16
  3. 4x² − 25
  4. 9a² + 48a + 64
  5. 25y² − 20y + 4
  6. 4y² + 4y + 1
  7. 16a² − 40a + 25
  8. 25x² − 49
  9. 16m² + 8m + 1
  10. 25x² + 80x + 64

Expand the cube

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

Expand using (a + b)³.

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

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.