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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 79

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 79
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 79
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 79
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 54 × 46
  2. Use an identity to find 101 × 102
  3. Use an identity to find 998²
  4. Use an identity to find 106 × 107
  5. Use an identity to find 1008 × 992
  6. Use an identity to find 993²
  7. Use an identity to find 59 × 60
  8. Use an identity to find 56 × 44
  9. Use an identity to find 59²
  10. Use an identity to find 52²

Factorise using identities

Class 9 · Worksheet 4 · set 79
Name:Date:Score:    / 10

Factorise.

  1. y² + 16y + 64
  2. 16x² − 9
  3. 9a² − 16
  4. 16x² + 72x + 81
  5. 4m² − 1
  6. 16x² − 1
  7. x² − 25
  8. m² − 6m + 9
  9. y² − 10y + 25
  10. 9x² − 12x + 4

Expand the cube

Class 9 · Worksheet 5 · set 79
Name:Date:Score:    / 8

Expand using (a + b)³.

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

Yes — press “▶️ Practise online” on any worksheet. The questions come one at a time with instant marking, a score at the end and a review of mistakes. No sign-in is needed.