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

Short cut cubing of any two 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 two digit number

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

Where, d will always be one of the numbers (+/-)1, (+/-)2, (+/-)3, (+/-)4, (+/-)5.

So, 3d2 will always be one of the numbers 3, 12, 27, 48, or 75.

For example,

To find cube of the number 23,

Let, z = 20 and d = 3

So,

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

(20 + 3)³ = 20 x [20 x (20 + 3(3)) + 3(3)²] + (3)³

(23)³ = 20 x [20 x (20 + 9) + 27] + (3)³

= 20 x [20 x 29 + 27] + (3)³

= 20 x [580 + 27] + (3)³

= 20 x 607 + (3)³

= 12140 + 27

= 12167

Another example,

To find cube of the number 88,

Let, z = 90 and d = (-2)

So,

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

(90 + (-2)) ³ = 90 x [90 x (90 + 3(-2)) + 3(-2)²] + (-2)³

(88)³ = 90 x [90 x (90 + (-6)) + 12] + (-2)³

= 90 x [90 x 84 + 12] + (-2)³

= 90 x [7560 + 12] + (-2)³

= 90 x 7572 + (-2)³

= 681480 + (-8)

= 681472

Short cut cubing of any two digit number just in few seconds with help of algebraic identity

We can utilize following algebraic identity to easily find cube of any two digit number

A³ = (A - d) x A x (A + d) + d² x A

Where, d = any assumed value to easily compute cube.

Naturally, this formula works for any value of d, but we choose d to be the distance to a number close to A that is easy to multiply.
For example,

To find cube of the number 23,

Let, d = 3, A = 23

So,

A³ = (A - d) x A x (A + d) + d² x A

= (23 - 3) x 23 x (23 + 3) + (3)² x 23

= 20 x 23 x 26 + (3)² x 23

= 20 x 598 + 9 x 23

= 11960 + 207

= 12167