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 13

Name:Date:Score: / 10

Expand using (a + b)² or (a − b)².

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

with answer key

(a + b)(a − b)

Class 8–9 · Worksheet 2 · set 13

Name:Date:Score: / 10

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

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

with answer key

Calculate with identities

Class 8–9 · Worksheet 3 · set 13

Name:Date:Score: / 10

Use an identity — no long multiplication.

Use an identity to find 55²
Use an identity to find 1004²
Use an identity to find 106 × 107
Use an identity to find 95 × 96
Use an identity to find 54 × 46
Use an identity to find 42 × 43
Use an identity to find 51 × 49
Use an identity to find 44²
Use an identity to find 98²
Use an identity to find 1001 × 999

with answer key

Factorise using identities

Class 9 · Worksheet 4 · set 13

Name:Date:Score: / 10

Factorise.

y² − 36
16y² + 56y + 49
4a² − 4a + 1
25x² + 60x + 36
25x² − 36
m² − 8m + 16
25a² − 60a + 36
m² + 10m + 25
4m² + 20m + 25
y² − 9

with answer key

Expand the cube

Class 9 · Worksheet 5 · set 13

Name:Date:Score: / 8

Expand using (a + b)³.

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

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

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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