Apps

TalentJR apps

How the apps work →
Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 75

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 75
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 75
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 75
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 59 × 41
  2. Use an identity to find 104²
  3. Use an identity to find 1003 × 997
  4. Use an identity to find 1007 × 993
  5. Use an identity to find 95 × 96
  6. Use an identity to find 42²
  7. Use an identity to find 107²
  8. Use an identity to find 1005²
  9. Use an identity to find 59²
  10. Use an identity to find 57 × 58

Factorise using identities

Class 9 · Worksheet 4 · set 75
Name:Date:Score:    / 10

Factorise.

  1. 4x² − 9
  2. 25y² + 70y + 49
  3. 4y² − 81
  4. a² − 14a + 49
  5. 4x² − 36x + 81
  6. 16y² − 25
  7. 25x² + 90x + 81
  8. 9x² − 42x + 49
  9. y² + 6y + 9
  10. 9m² − 4

Expand the cube

Class 9 · Worksheet 5 · set 75
Name:Date:Score:    / 8

Expand using (a + b)³.

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