Algebra Formulas Sheet — Identities with Practice

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(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 9

Name:Date:Score: / 10

Expand using (a + b)² or (a − b)².

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

with answer key

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 9

Name:Date:Score: / 10

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

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

with answer key

Calculate with identities

Class 8–9 · Worksheet 3 · set 9

Name:Date:Score: / 10

Use an identity — no long multiplication.

Use an identity to find 108 × 92
Use an identity to find 49²
Use an identity to find 1008 × 992
Use an identity to find 1005 × 995
Use an identity to find 101 × 99
Use an identity to find 106 × 94
Use an identity to find 104 × 96
Use an identity to find 57 × 58
Use an identity to find 992²
Use an identity to find 107 × 93

with answer key

Factorise using identities

Class 9 · Worksheet 4 · set 9

Name:Date:Score: / 10

Factorise.

4y² + 28y + 49
16x² − 25
25m² − 9
x² − 16
16y² − 24y + 9
4a² + 4a + 1
4m² + 12m + 9
25y² + 20y + 4
4y² + 20y + 25
y² − 36

with answer key

Expand the cube

Class 9 · Worksheet 5 · set 9

Name:Date:Score: / 8

Expand using (a + b)³.

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

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Press “🔄 New set” — the questions change (maths numbers are new every time; English sentences are shuffled).

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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