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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 4

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 4
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 4
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 4
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 47 × 48
  2. Use an identity to find 95 × 96
  3. Use an identity to find 1009 × 991
  4. Use an identity to find 58²
  5. Use an identity to find 54²
  6. Use an identity to find 51 × 52
  7. Use an identity to find 1008 × 992
  8. Use an identity to find 1002²
  9. Use an identity to find 49²
  10. Use an identity to find 101 × 102

Factorise using identities

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

Factorise.

  1. 4y² + 4y + 1
  2. x² − 14x + 49
  3. 4a² + 12a + 9
  4. 16y² − 49
  5. 4y² − 4y + 1
  6. m² − 4
  7. 25x² + 80x + 64
  8. 25y² + 90y + 81
  9. 25m² − 40m + 16
  10. a² − 8a + 16

Expand the cube

Class 9 · Worksheet 5 · set 4
Name:Date:Score:    / 8

Expand using (a + b)³.

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