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

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 8
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

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

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

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

Calculate with identities

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

Use an identity — no long multiplication.

  1. Use an identity to find 993²
  2. Use an identity to find 108 × 92
  3. Use an identity to find 92 × 93
  4. Use an identity to find 95 × 96
  5. Use an identity to find 1006 × 994
  6. Use an identity to find 995²
  7. Use an identity to find 1009 × 991
  8. Use an identity to find 46 × 47
  9. Use an identity to find 107²
  10. Use an identity to find 59 × 41

Factorise using identities

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

Factorise.

  1. 9x² + 48x + 64
  2. 9a² − 30a + 25
  3. 25x² + 40x + 16
  4. 4a² − 9
  5. y² + 2y + 1
  6. 16a² − 56a + 49
  7. x² − 64
  8. 9m² − 4
  9. 25x² − 90x + 81
  10. 25m² − 20m + 4

Expand the cube

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

Expand using (a + b)³.

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