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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 15

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 15
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 15
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 15
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 57 × 43
  2. Use an identity to find 1004²
  3. Use an identity to find 57²
  4. Use an identity to find 1009²
  5. Use an identity to find 56 × 44
  6. Use an identity to find 102 × 98
  7. Use an identity to find 57 × 58
  8. Use an identity to find 104²
  9. Use an identity to find 109 × 91
  10. Use an identity to find 1002 × 998

Factorise using identities

Class 9 · Worksheet 4 · set 15
Name:Date:Score:    / 10

Factorise.

  1. m² − 49
  2. 4m² − 9
  3. 9x² − 48x + 64
  4. 16x² + 24x + 9
  5. a² − 10a + 25
  6. 16a² − 81
  7. 4a² − 49
  8. 9y² − 30y + 25
  9. 25x² + 90x + 81
  10. 16m² − 24m + 9

Expand the cube

Class 9 · Worksheet 5 · set 15
Name:Date:Score:    / 8

Expand using (a + b)³.

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