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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 40

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 40
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 40
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 40
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 47 × 48
  2. Use an identity to find 1002 × 998
  3. Use an identity to find 104 × 96
  4. Use an identity to find 41²
  5. Use an identity to find 51 × 49
  6. Use an identity to find 997²
  7. Use an identity to find 56 × 44
  8. Use an identity to find 53 × 54
  9. Use an identity to find 98²
  10. Use an identity to find 106²

Factorise using identities

Class 9 · Worksheet 4 · set 40
Name:Date:Score:    / 10

Factorise.

  1. y² − 49
  2. 25m² − 64
  3. 16x² − 40x + 25
  4. x² − 16
  5. 25m² + 40m + 16
  6. 4x² + 12x + 9
  7. y² − 12y + 36
  8. 4x² − 12x + 9
  9. 4x² + 28x + 49
  10. y² − 81

Expand the cube

Class 9 · Worksheet 5 · set 40
Name:Date:Score:    / 8

Expand using (a + b)³.

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