Apps

TalentJR apps

How the apps work →
Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 68

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.

💡 Learn it first

🧮 The worksheets

🔄 New set of questions

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 68
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 68
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 68
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 53 × 47
  2. Use an identity to find 54²
  3. Use an identity to find 102 × 98
  4. Use an identity to find 107 × 93
  5. Use an identity to find 103 × 104
  6. Use an identity to find 102²
  7. Use an identity to find 41 × 42
  8. Use an identity to find 43²
  9. Use an identity to find 106 × 94
  10. Use an identity to find 55 × 45

Factorise using identities

Class 9 · Worksheet 4 · set 68
Name:Date:Score:    / 10

Factorise.

  1. 25x² − 80x + 64
  2. 25y² − 30y + 9
  3. 25x² − 16
  4. 4x² − 28x + 49
  5. m² − 49
  6. 9a² + 48a + 64
  7. x² − 1
  8. 16x² − 40x + 25
  9. 25y² − 10y + 1
  10. 25a² − 40a + 16

Expand the cube

Class 9 · Worksheet 5 · set 68
Name:Date:Score:    / 8

Expand using (a + b)³.

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

More worksheets

📈 Polynomials worksheet🔤 Algebraic expressions⚡ Exponents and powers Noun worksheetsPronoun worksheetsArticles worksheetTenses worksheetPrepositions worksheetSubtraction worksheets All worksheets

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.

How do I get different questions?

Press “🔄 New set” — the questions change (maths numbers are new every time; English sentences are shuffled).

How do I print only one worksheet?

Press “🖨️ Print” on that worksheet. Tick “with answer key” if you want the answers on a second page.

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.