📘 Math: Squares, Cubes & Identities

🔷 TOPIC: SQUARE (n²)

A square means multiplying a number by itself.
Example: 2 × 2 = 4
So, square of 2 is 4.

Number	Square
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100
11	121
12	144
13	169
14	196
15	225
16	256
17	289
18	324
19	361
20	400

🔶 TOPIC: CUBE (n³)

A cube means multiplying a number three times.
Example: 2 × 2 × 2 = 8
So, cube of 2 is 8.

Number	Cube
1	1
2	8
3	27
4	64
5	125
6	216
7	343
8	512
9	729
10	1000
11	1331
12	1728
13	2197
14	2744
15	3375
16	4096
17	4913
18	5832
19	6859
20	8000

📐 TOPIC: IDENTITIES

Identities are formulas that always work and make math easy!

📘 Identities with Clear Diagrams

1. (a + b)²

This is a big square of side (a + b)

a²

ab

ab

b²

(a + b)² = a² + 2ab + b²

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2. (a - b)²

Start with big square and remove parts

(a - b)² = a² - 2ab + b²

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3. a² - b²

Big square minus small square inside

b²

a² - b² = (a - b)(a + b)

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4. (a + b)³

Think of a cube made of blocks:

a³ + 3a²b + 3ab² + b³

(a + b)³ = a³ + 3a²b + 3ab² + b³

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5. (a - b)³

a³ - 3a²b + 3ab² - b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

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6. (a + b + c)²

a² + b² + c² + 2ab + 2bc + 2ca

(a + b + c)²

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a - b)(a + b)

(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