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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 30

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 30
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 30
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 30
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 1001²
  2. Use an identity to find 995²
  3. Use an identity to find 994²
  4. Use an identity to find 44 × 45
  5. Use an identity to find 43 × 44
  6. Use an identity to find 92 × 93
  7. Use an identity to find 109 × 91
  8. Use an identity to find 993²
  9. Use an identity to find 52²
  10. Use an identity to find 59²

Factorise using identities

Class 9 · Worksheet 4 · set 30
Name:Date:Score:    / 10

Factorise.

  1. 9m² − 42m + 49
  2. 4x² − 28x + 49
  3. 25a² − 10a + 1
  4. 9y² − 25
  5. x² + 16x + 64
  6. 16a² − 56a + 49
  7. m² + 2m + 1
  8. 25m² + 80m + 64
  9. 4x² + 28x + 49
  10. x² − 16x + 64

Expand the cube

Class 9 · Worksheet 5 · set 30
Name:Date:Score:    / 8

Expand using (a + b)³.

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

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.