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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 31

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 31
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 31
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 31
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 1009²
  2. Use an identity to find 1006 × 994
  3. Use an identity to find 993²
  4. Use an identity to find 1005 × 995
  5. Use an identity to find 48 × 49
  6. Use an identity to find 1003 × 997
  7. Use an identity to find 105 × 95
  8. Use an identity to find 56 × 44
  9. Use an identity to find 59 × 41
  10. Use an identity to find 1004 × 996

Factorise using identities

Class 9 · Worksheet 4 · set 31
Name:Date:Score:    / 10

Factorise.

  1. m² − 9
  2. 25a² − 36
  3. m² − 16
  4. 25x² − 60x + 36
  5. 4m² − 20m + 25
  6. 16x² − 40x + 25
  7. m² − 12m + 36
  8. 4x² − 9
  9. 25a² − 20a + 4
  10. m² − 4

Expand the cube

Class 9 · Worksheet 5 · set 31
Name:Date:Score:    / 8

Expand using (a + b)³.

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