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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 39

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 39
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 39
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 39
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 47²
  2. Use an identity to find 1001 × 999
  3. Use an identity to find 41 × 42
  4. Use an identity to find 107 × 93
  5. Use an identity to find 104 × 96
  6. Use an identity to find 49²
  7. Use an identity to find 1001²
  8. Use an identity to find 45 × 46
  9. Use an identity to find 103 × 104
  10. Use an identity to find 109 × 91

Factorise using identities

Class 9 · Worksheet 4 · set 39
Name:Date:Score:    / 10

Factorise.

  1. a² − 6a + 9
  2. y² + 18y + 81
  3. 9y² − 6y + 1
  4. 4y² − 12y + 9
  5. 16a² + 56a + 49
  6. 25x² + 90x + 81
  7. x² − 2x + 1
  8. a² − 10a + 25
  9. 4m² − 4m + 1
  10. m² − 8m + 16

Expand the cube

Class 9 · Worksheet 5 · set 39
Name:Date:Score:    / 8

Expand using (a + b)³.

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

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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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