Apps

TalentJR apps

How the apps work →
Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 65

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 65
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 65
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 65
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 92 × 93
  2. Use an identity to find 51²
  3. Use an identity to find 58²
  4. Use an identity to find 97²
  5. Use an identity to find 105 × 95
  6. Use an identity to find 99 × 100
  7. Use an identity to find 54 × 55
  8. Use an identity to find 55 × 56
  9. Use an identity to find 52 × 53
  10. Use an identity to find 51 × 52

Factorise using identities

Class 9 · Worksheet 4 · set 65
Name:Date:Score:    / 10

Factorise.

  1. 4m² + 36m + 81
  2. y² + 18y + 81
  3. 16m² + 24m + 9
  4. 9a² − 30a + 25
  5. 16a² − 25
  6. 25m² + 90m + 81
  7. a² − 6a + 9
  8. 25m² − 20m + 4
  9. m² − 18m + 81
  10. m² − 36

Expand the cube

Class 9 · Worksheet 5 · set 65
Name:Date:Score:    / 8

Expand using (a + b)³.

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