Question

can anyone pls explain this pattern
I m not able to understand it properly ​

Answer 1

Answer:

Just a use of a³ - b³ = (a - b)(a² + ab + b²)

Step-by-step explanation:

       IN GENERAL:

Using the formula:

   a³ - b³ = (a - b)(a² + ab + b²)

For any two consecutive numbers 'x' and 'x + 1'.

⇒ (x + 1)³ - x³

⇒ (x+1 - x)[ (x + 1)² + x(x + 1) + x² ]

⇒ (1) [ (x² + 1 + 2x) + (x² + x) + x² ]

⇒ [ x² + 1 + 2x + x² + x + x² ]

⇒ 1 + 3x² + 3x

⇒ 1 + 3x(x + 1)  , as 3 and x are multiplied, we can write it as 1 + (x + 1)×x×3

        this is what being used here.

For x = 1

2³ - 1³ = 1 + (1 + 2) × 1 × 3

           = 1 + 1 × 2 × 3

For x = 2,

3³ - 2³ = 1 + (2 + 1) × (2) × 3

           = 1 + 3 × 2 × 3

So on.