Apps

TalentJR apps

How the apps work →
Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 76

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 76
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 76
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 76
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 1005 × 995
  2. Use an identity to find 49 × 50
  3. Use an identity to find 58 × 59
  4. Use an identity to find 91 × 92
  5. Use an identity to find 48 × 49
  6. Use an identity to find 54 × 55
  7. Use an identity to find 107²
  8. Use an identity to find 1003²
  9. Use an identity to find 1001 × 999
  10. Use an identity to find 109 × 91

Factorise using identities

Class 9 · Worksheet 4 · set 76
Name:Date:Score:    / 10

Factorise.

  1. x² − 10x + 25
  2. 25x² − 10x + 1
  3. 4y² − 1
  4. 25x² + 80x + 64
  5. 16a² − 8a + 1
  6. 16a² + 56a + 49
  7. 25a² − 20a + 4
  8. 25x² + 60x + 36
  9. 9x² + 48x + 64
  10. a² − 9

Expand the cube

Class 9 · Worksheet 5 · set 76
Name:Date:Score:    / 8

Expand using (a + b)³.

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