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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 27

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 27
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 27
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 27
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 996²
  2. Use an identity to find 108 × 92
  3. Use an identity to find 42 × 43
  4. Use an identity to find 1002 × 998
  5. Use an identity to find 41²
  6. Use an identity to find 1003 × 997
  7. Use an identity to find 101 × 99
  8. Use an identity to find 43²
  9. Use an identity to find 106 × 107
  10. Use an identity to find 1007²

Factorise using identities

Class 9 · Worksheet 4 · set 27
Name:Date:Score:    / 10

Factorise.

  1. 25x² − 70x + 49
  2. 16a² − 40a + 25
  3. 4a² + 36a + 81
  4. 4m² − 81
  5. 9m² − 49
  6. 25m² + 40m + 16
  7. x² − 36
  8. y² + 2y + 1
  9. a² − 14a + 49
  10. x² − 49

Expand the cube

Class 9 · Worksheet 5 · set 27
Name:Date:Score:    / 8

Expand using (a + b)³.

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