Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 41

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 41
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 41
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 41
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 53 × 47
  2. Use an identity to find 106²
  3. Use an identity to find 96²
  4. Use an identity to find 92²
  5. Use an identity to find 995²
  6. Use an identity to find 102²
  7. Use an identity to find 1003²
  8. Use an identity to find 997²
  9. Use an identity to find 58 × 42
  10. Use an identity to find 52²

Factorise using identities

Class 9 · Worksheet 4 · set 41
Name:Date:Score:    / 10

Factorise.

  1. 25a² + 80a + 64
  2. 16x² − 81
  3. x² − 81
  4. 9y² + 48y + 64
  5. 4x² + 4x + 1
  6. 16m² − 24m + 9
  7. 25y² − 80y + 64
  8. 16y² − 24y + 9
  9. 25m² − 16
  10. 16a² + 56a + 49

Expand the cube

Class 9 · Worksheet 5 · set 41
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 − 1)³
  6. (x − 5)³
  7. (x + 5)³
  8. (x + 2)³

More worksheets

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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