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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 85

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 85
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 85
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 85
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 46 × 47
  2. Use an identity to find 996²
  3. Use an identity to find 57 × 43
  4. Use an identity to find 1001 × 999
  5. Use an identity to find 98²
  6. Use an identity to find 104 × 105
  7. Use an identity to find 999²
  8. Use an identity to find 1003²
  9. Use an identity to find 104 × 96
  10. Use an identity to find 1004 × 996

Factorise using identities

Class 9 · Worksheet 4 · set 85
Name:Date:Score:    / 10

Factorise.

  1. 16y² + 72y + 81
  2. 25m² + 10m + 1
  3. 9y² + 42y + 49
  4. 16m² + 72m + 81
  5. 25x² − 30x + 9
  6. 16y² − 81
  7. 25m² − 80m + 64
  8. a² + 2a + 1
  9. x² − 2x + 1
  10. 4x² + 28x + 49

Expand the cube

Class 9 · Worksheet 5 · set 85
Name:Date:Score:    / 8

Expand using (a + b)³.

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