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 74

Name:Date:Score: / 10

Expand using (a + b)² or (a − b)².

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

with answer key

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 74

Name:Date:Score: / 10

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

(4x + 4)(4x − 4)
(4y + 5)(4y − 5)
(2a + 4)(2a − 4)
(2a + 5)(2a − 5)
(5m + 5)(5m − 5)
(3m + 5)(3m − 5)
(3y + 7)(3y − 7)
(3m + 8)(3m − 8)
(3m + 9)(3m − 9)
(5y + 2)(5y − 2)

with answer key

Calculate with identities

Class 8–9 · Worksheet 3 · set 74

Name:Date:Score: / 10

Use an identity — no long multiplication.

Use an identity to find 42 × 43
Use an identity to find 109 × 91
Use an identity to find 47 × 48
Use an identity to find 108²
Use an identity to find 94²
Use an identity to find 1002 × 998
Use an identity to find 43 × 44
Use an identity to find 54 × 46
Use an identity to find 996²
Use an identity to find 41 × 42

with answer key

Factorise using identities

Class 9 · Worksheet 4 · set 74

Name:Date:Score: / 10

Factorise.

a² − 14a + 49
y² − 8y + 16
25m² + 10m + 1
m² − 36
9y² − 48y + 64
m² − 6m + 9
a² − 16a + 64
16a² + 56a + 49
25x² − 9
25a² − 40a + 16

with answer key

Expand the cube

Class 9 · Worksheet 5 · set 74

Name:Date:Score: / 8

Expand using (a + b)³.

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