# Cubing (Magic – Math’s tricks)

### Calculate cube in a second…

**Math’s tricks and shortcuts are the easiest and fastest ways in which you can solve mathematical problems in ****any ****upcoming Government exams**** ****SSC, BANK , RAILWAY, UPSC****,**** CIVIL SERVICES****, Railway, CAT, NDA, etc.**

The quantitative aptitude or the numerical ability section are most commonly a part of all major Government exams and if a candidate can get shortcut tricks to solve this section quickly he may be able to score more overall in the examination.

Today, we will see two tricks to calculate the cube of any number.

__Method I__

__Method I__

#### The method is based on the algebraic observation that

*A*^{3}** ****=** **(***A –* *d***) * ***A * ***(***A +* *d***) +** *d*^{2}*A*

*A*

^{3}

*A –*

*d*

*A **

*A +*

*d*

*d*

^{2}

*A*

where *d *is any number, the distance to the nearest multiple of ten.

For example, when cubing 13, we let *d **= *3 as 13 – 3 = 10 that is nearest multiple of 10, resulting in:

13^{3 }= (13 – 3) * 13 ( 13 + 3) + (3^{2} * 13)

= 10 * 13 * 16 + (9 * 13)

= 10 * (1 (6+3) 18) + 117 [ Used Criss-Cross System, Vedic method]

= 10 * 208 + 117

= 2080 +117

= 2197 is the correct answer.

**Let’****s take another example**, 35^{3 }= ?^{}

Let d= 5, as 35-5 = 30 that is nearest multiple of 10.

So,

35^{3} = (30 * 35 * 40 ) + 5^{2} * 35

= ( 30 * 1400) + (25 * 35)

Here, use Criss-Cross System, Vedic method to solve the 2 digits multiplication.

= ( 42000 ) + [6 (10 + 15) 25]

= 42000 + ( 6 (25) 25) )

= 42000 + 875

= 42,875 is the answer.

What is 92^{3}?

Let’s take d = 2,

923 = ( 90 * 92 * 94) + (4 * 92)

= ( 90 * 8648) + 368

Used Criss-Cross method to solve 92 * 94

= 778320 + 368

= 778,688 is the answer.

__Method II__

#### The next method is based on the below algebraic observation

(ab)^{3} = a^{3} | 3 a^{2}b | 3ab^{2} | b^{3}

Now, let’s find the cube of 13?

As we can see, number is 13, so here a = 1 and b = 3

So, let’s put the value of a and b in the algebraic observation

(13)^{3} =1^{3} | 3 * 1^{2} * 3 | 3 * 1 * 3^{2} | 3^{3}

= 1 | 9 | 27 | 27

=2197 is the answer.

Enjoy reading…keep learning…