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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 47

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 47
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 47
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 47
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 44²
  2. Use an identity to find 52 × 48
  3. Use an identity to find 55 × 45
  4. Use an identity to find 55²
  5. Use an identity to find 46 × 47
  6. Use an identity to find 1007²
  7. Use an identity to find 105 × 95
  8. Use an identity to find 52²
  9. Use an identity to find 1005²
  10. Use an identity to find 54 × 55

Factorise using identities

Class 9 · Worksheet 4 · set 47
Name:Date:Score:    / 10

Factorise.

  1. 4a² + 20a + 25
  2. 4x² + 20x + 25
  3. y² − 16
  4. 9y² + 48y + 64
  5. a² − 8a + 16
  6. y² − 49
  7. 9x² − 64
  8. 16x² − 25
  9. x² − 36
  10. y² − 1

Expand the cube

Class 9 · Worksheet 5 · set 47
Name:Date:Score:    / 8

Expand using (a + b)³.

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