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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 36

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 36
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 36
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 36
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 996²
  2. Use an identity to find 104 × 96
  3. Use an identity to find 106²
  4. Use an identity to find 42 × 43
  5. Use an identity to find 55 × 56
  6. Use an identity to find 106 × 107
  7. Use an identity to find 101 × 102
  8. Use an identity to find 1007 × 993
  9. Use an identity to find 55²
  10. Use an identity to find 107 × 108

Factorise using identities

Class 9 · Worksheet 4 · set 36
Name:Date:Score:    / 10

Factorise.

  1. 9y² + 30y + 25
  2. 25a² − 80a + 64
  3. m² − 4m + 4
  4. 9y² + 48y + 64
  5. 25y² − 30y + 9
  6. 25y² − 40y + 16
  7. m² − 2m + 1
  8. 16m² − 1
  9. x² − 8x + 16
  10. 25m² − 90m + 81

Expand the cube

Class 9 · Worksheet 5 · set 36
Name:Date:Score:    / 8

Expand using (a + b)³.

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

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