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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 80

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 80
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 80
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 80
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 105 × 95
  2. Use an identity to find 94²
  3. Use an identity to find 999²
  4. Use an identity to find 997²
  5. Use an identity to find 54 × 55
  6. Use an identity to find 96 × 97
  7. Use an identity to find 1004 × 996
  8. Use an identity to find 55 × 45
  9. Use an identity to find 104²
  10. Use an identity to find 996²

Factorise using identities

Class 9 · Worksheet 4 · set 80
Name:Date:Score:    / 10

Factorise.

  1. 25y² − 36
  2. m² + 16m + 64
  3. 9m² − 4
  4. 4x² − 28x + 49
  5. 9m² − 16
  6. 25y² − 20y + 4
  7. a² + 8a + 16
  8. m² + 4m + 4
  9. 4m² − 4m + 1
  10. 4a² + 36a + 81

Expand the cube

Class 9 · Worksheet 5 · set 80
Name:Date:Score:    / 8

Expand using (a + b)³.

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