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

Quick multiplication of any two digit number near to each other with help of algebraic close together method

We can utilize following algebraic identity for quick multiplication of any two digit number which are near to each other

(z + a) x (z + b) = z x (z + a + b) + a x b

Where, z = any number ends with zero.

For example,

To multiply 23 x 26,

Let, z = 20, a = 3, b = 6

So, 

(z + a) x (z + b) 

= z x (z + a + b) + a x b

= 20 x (20 + 3 + 6) + 3 x 6

= 20 x 29 + 3 x 6

= 580 + 18

= 598

Another example,

To multiply 88 x 86,

Let, z = 80, a = 8, b = 6

So, 

(z + a) x (z + b) 

= z x (z + a + b) + a x b

= 80 x (80 + 8 + 6) + 8 x 6

= 80 x 94 + 8 x 6

= 7520 + 48

= 7568