Apps

TalentJR apps

How the apps work →
Free · Class 8–10 · 5 worksheets · answer keys · practise online · set 77

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 77
Name:Date:Score:    / 10

Expand using (a + b)² or (a − b)².

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

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 77
Name:Date:Score:    / 10

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

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

Calculate with identities

Class 8–9 · Worksheet 3 · set 77
Name:Date:Score:    / 10

Use an identity — no long multiplication.

  1. Use an identity to find 999²
  2. Use an identity to find 58 × 59
  3. Use an identity to find 992²
  4. Use an identity to find 98²
  5. Use an identity to find 103 × 97
  6. Use an identity to find 1001 × 999
  7. Use an identity to find 1007 × 993
  8. Use an identity to find 1008 × 992
  9. Use an identity to find 42 × 43
  10. Use an identity to find 1007²

Factorise using identities

Class 9 · Worksheet 4 · set 77
Name:Date:Score:    / 10

Factorise.

  1. 25a² + 90a + 81
  2. 4m² − 36m + 81
  3. 25m² − 30m + 9
  4. 4y² + 12y + 9
  5. 9a² − 12a + 4
  6. a² + 16a + 64
  7. 25y² + 30y + 9
  8. 25m² − 9
  9. y² − 18y + 81
  10. 25m² − 49

Expand the cube

Class 9 · Worksheet 5 · set 77
Name:Date:Score:    / 8

Expand using (a + b)³.

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