Short cut cubing of any three digit number just in few seconds with help of Horner`s method for polynomial evaluation

We can utilize following algebraic expansion of Horner`s method for polynomial evaluation to easily find cube of any three digit number

(z + d) ³ = z x [z x (z + 3d) + 3d²] + d³

Where, d will always be one of the numbers between (+/-) 1 to (+/-) 50.

For example,

To find cube of the number 323,

Let, z = 300 and d = 23

So,

(z + d) ³ = z x [z x (z + 3d) + 3d²] + d³

(300 + (23)) ³ = 300 x [300 x (300 + 3(23)) + 3(23)²] + (23)³

(323)³ = 300 x [300 x (300 + 69) + 3(23)²] + (23)³

= 300 x [300 x 369 + 3(23)²] + (23)³

= 300 x [300 x 369 + 1587] + (23)³

= 300 x [110700 + 1587] + (23)³

= 300 x 112287 + (23)³

= 33686100 + 12167

= 33698267