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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 11

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 11
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 11
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 11
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 109 × 91
  2. Use an identity to find 47 × 48
  3. Use an identity to find 998²
  4. Use an identity to find 1002²
  5. Use an identity to find 991²
  6. Use an identity to find 98 × 99
  7. Use an identity to find 104 × 96
  8. Use an identity to find 91²
  9. Use an identity to find 1006 × 994
  10. Use an identity to find 102 × 98

Factorise using identities

Class 9 · Worksheet 4 · set 11
Name:Date:Score:    / 10

Factorise.

  1. y² − 4
  2. 16m² + 56m + 49
  3. 25a² + 20a + 4
  4. 16m² − 40m + 25
  5. 25x² + 40x + 16
  6. 25y² − 40y + 16
  7. a² − 8a + 16
  8. 9x² − 24x + 16
  9. 9y² − 42y + 49
  10. y² − 1

Expand the cube

Class 9 · Worksheet 5 · set 11
Name:Date:Score:    / 8

Expand using (a + b)³.

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