Algebra Formulas Sheet — Identities with Practice

💡 Learn it first

(a + b)² = a² + 2ab + b² · (a − b)² = a² − 2ab + b² · (a + b)(a − b) = a² − b²

(x + a)(x + b) = x² + (a + b)x + ab · (a + b)³ = a³ + 3a²b + 3ab² + b³ · (a − b)³ = a³ − 3a²b + 3ab² − b³

a³ + b³ = (a + b)(a² − ab + b²) · a³ − b³ = (a − b)(a² + ab + b²) · (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Use them to calculate fast: 103² = (100 + 3)² = 10000 + 600 + 9 = 10609; 52 × 48 = (50 + 2)(50 − 2) = 2500 − 4 = 2496.

Expand the square

Class 8–9 · Worksheet 1 · set 25

Name:Date:Score: / 10

Expand using (a + b)² or (a − b)².

(2a − 3)²
(5x + 4)²
(5y − 4)²
(x + 8)²
(4m − 1)²
(y + 4)²
(2a − 9)²
(5y + 4)²
(4x − 5)²
(m − 1)²

with answer key

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 25

Name:Date:Score: / 10

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

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

with answer key

Calculate with identities

Class 8–9 · Worksheet 3 · set 25

Name:Date:Score: / 10

Use an identity — no long multiplication.

Use an identity to find 55 × 45
Use an identity to find 43 × 44
Use an identity to find 108 × 109
Use an identity to find 109 × 91
Use an identity to find 106 × 94
Use an identity to find 46 × 47
Use an identity to find 104²
Use an identity to find 1006 × 994
Use an identity to find 1007 × 993
Use an identity to find 48²

with answer key

Factorise using identities

Class 9 · Worksheet 4 · set 25

Name:Date:Score: / 10

Factorise.

4x² + 12x + 9
a² − 1
16m² + 56m + 49
x² − 16
9x² + 12x + 4
4x² − 1
4y² + 28y + 49
25x² − 9
16x² − 72x + 81
x² − 81

with answer key

Expand the cube

Class 9 · Worksheet 5 · set 25

Name:Date:Score: / 8

Expand using (a + b)³.

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

with answer key

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.

Algebra formulas sheet — identities, with practice questions

💡 Learn it first

🧮 The worksheets

Expand the square

✅ Answer key — Expand the square

(a + b)(a − b)

✅ Answer key — (a + b)(a − b)

Calculate with identities

✅ Answer key — Calculate with identities

Factorise using identities

✅ Answer key — Factorise using identities

Expand the cube

✅ Answer key — Expand the cube

More worksheets

Questions