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Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 46

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 46
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 46
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 46
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 993²
  2. Use an identity to find 56 × 44
  3. Use an identity to find 54 × 55
  4. Use an identity to find 52²
  5. Use an identity to find 105²
  6. Use an identity to find 93 × 94
  7. Use an identity to find 107 × 108
  8. Use an identity to find 994²
  9. Use an identity to find 96 × 97
  10. Use an identity to find 1007 × 993

Factorise using identities

Class 9 · Worksheet 4 · set 46
Name:Date:Score:    / 10

Factorise.

  1. 9x² + 48x + 64
  2. 25x² + 20x + 4
  3. x² − 64
  4. 25a² − 10a + 1
  5. 16a² + 8a + 1
  6. 9a² + 24a + 16
  7. 4m² − 25
  8. 16m² − 56m + 49
  9. 4x² − 4x + 1
  10. 16a² − 72a + 81

Expand the cube

Class 9 · Worksheet 5 · set 46
Name:Date:Score:    / 8

Expand using (a + b)³.

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

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