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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 44

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 44
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 44
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 44
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 58 × 42
  2. Use an identity to find 51²
  3. Use an identity to find 49 × 50
  4. Use an identity to find 52 × 53
  5. Use an identity to find 51 × 49
  6. Use an identity to find 55 × 45
  7. Use an identity to find 59 × 41
  8. Use an identity to find 107²
  9. Use an identity to find 108 × 109
  10. Use an identity to find 103 × 97

Factorise using identities

Class 9 · Worksheet 4 · set 44
Name:Date:Score:    / 10

Factorise.

  1. 9y² − 42y + 49
  2. 16m² − 24m + 9
  3. 25y² − 30y + 9
  4. 9x² + 48x + 64
  5. 25y² + 60y + 36
  6. 16x² − 72x + 81
  7. 9y² + 6y + 1
  8. 25a² + 30a + 9
  9. m² − 1
  10. 4x² − 9

Expand the cube

Class 9 · Worksheet 5 · set 44
Name:Date:Score:    / 8

Expand using (a + b)³.

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

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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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