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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 28

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 28
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 28
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 28
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 1004²
  2. Use an identity to find 48 × 49
  3. Use an identity to find 108 × 109
  4. Use an identity to find 106²
  5. Use an identity to find 41²
  6. Use an identity to find 101²
  7. Use an identity to find 102 × 98
  8. Use an identity to find 1006 × 994
  9. Use an identity to find 49 × 50
  10. Use an identity to find 1006²

Factorise using identities

Class 9 · Worksheet 4 · set 28
Name:Date:Score:    / 10

Factorise.

  1. 9y² + 48y + 64
  2. 25y² + 80y + 64
  3. 4m² − 20m + 25
  4. y² − 49
  5. 4x² + 36x + 81
  6. 25m² − 16
  7. 9m² − 64
  8. 9x² − 49
  9. 16a² − 9
  10. 25x² + 80x + 64

Expand the cube

Class 9 · Worksheet 5 · set 28
Name:Date:Score:    / 8

Expand using (a + b)³.

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