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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 23

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 23
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 23
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 23
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 53 × 47
  2. Use an identity to find 1003 × 997
  3. Use an identity to find 93²
  4. Use an identity to find 92²
  5. Use an identity to find 994²
  6. Use an identity to find 49²
  7. Use an identity to find 1008²
  8. Use an identity to find 41²
  9. Use an identity to find 52 × 48
  10. Use an identity to find 91²

Factorise using identities

Class 9 · Worksheet 4 · set 23
Name:Date:Score:    / 10

Factorise.

  1. 9x² − 49
  2. y² + 4y + 4
  3. 4y² + 36y + 81
  4. 4m² − 28m + 49
  5. m² − 14m + 49
  6. 25m² + 70m + 49
  7. 9a² + 12a + 4
  8. 25x² + 70x + 49
  9. 4m² − 12m + 9
  10. 25m² + 60m + 36

Expand the cube

Class 9 · Worksheet 5 · set 23
Name:Date:Score:    / 8

Expand using (a + b)³.

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