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

Basic Concept Of Mathematical Multiplication Of Two Digit Numbers

This article discusses about basic concept of mathematical multiplication of two digit number and teaches you the basic and easy way to multiply any two digit numbers.    

The journey of multiplying two digit numbers begins with the basic understanding of multiplication process for two digit numbers.

Let’s start with example of multiplying 24 with 43...

            24 x 43 =?

Step 1: Multiply left most digits of the numbers.

            In our example left most digits are 4 and 3.

                        So, 4 x 3 = 12

Step 2: Cross multiply left most digit of each number with right most digit of other number and sum up the answer.

In our example left most digits 2 and 4 are multiplied with right most digits 3 and 4 respectively and sum up the answers.

            So,

            2 x 3 = 6

            4 x 4 = 16

            Finally,

            6 + 16 = 22

Step 3: Multiply right most digits of the numbers.

            In our example right most digits are 2 and 4.

                        So, 2 x 4 = 8

Step 4: Sum up answer of step 1 with answer of step 2 multiplied by 10 and answer of step 3 multiplied by 100.

In other words sum up answer of step 1 with answers of step 2 and step 3 respectively after adding one and two zeros respectively.

            In our example,

            The answer of step 1 is 12.

            The answer of step 2 is 22.

            The answer of step 3 is 8.

            So, 12 + (22x10) + (8x100) = 1032

            In other words, 12 + 220 + 800 = 1032

In this way the final answer of 24 x 43 = 1032.

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