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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 38

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 38
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 38
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 38
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 993²
  2. Use an identity to find 57²
  3. Use an identity to find 106 × 94
  4. Use an identity to find 55 × 45
  5. Use an identity to find 95 × 96
  6. Use an identity to find 58²
  7. Use an identity to find 1002²
  8. Use an identity to find 1006 × 994
  9. Use an identity to find 101 × 102
  10. Use an identity to find 53 × 54

Factorise using identities

Class 9 · Worksheet 4 · set 38
Name:Date:Score:    / 10

Factorise.

  1. 16y² − 81
  2. m² − 8m + 16
  3. x² + 10x + 25
  4. x² − 36
  5. 16a² − 49
  6. 9x² − 1
  7. m² − 10m + 25
  8. 16x² − 24x + 9
  9. 25y² + 40y + 16
  10. a² − 49

Expand the cube

Class 9 · Worksheet 5 · set 38
Name:Date:Score:    / 8

Expand using (a + b)³.

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