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Cubes

Here, you will learn how to calculate cubes of 2-digit numbers.

For this to be easy, you should know the cubes of numbers from 1 to 10. They are- 
1^3   =  1
2^3   =  8 
3^3   =  27 
4^3   =  64 
5^3   =  125
6^3   =  216
7^3   =  343
8^3   =  512
9^3   =  729 
10^3 =  1000



Calculating the cubes - 

Step 1: Divide the number in 2 parts. For example, if the number was 56, then part 1 would be 5 and the other part would be 6. For the sake of convenience, lets call the 2 parts as x and y. ( in 56, 5 is x and 6 is y. )

Step 2: Use formula x^3 | 3*x*x*y | 3*x*y*y | y^3. After substituting the values and multiplying the numbers, use the balancing rule to get the answer.

Examples- 
1. 12^3
Here, x = 1 and y = 2.
Using the formula, we have -
  1^3 | 3*1*1*2 | 3*1*2*2 | 2^3
= 01 | 06 | 12 | 08 
= 1728

2. 34^3
Here, x = 3 and y = 4.

Using the formula, we have -
  3^3 | 3*3*3*4 | 3*3*4*4 | 4^3
= 27 | 108 | 144 | 64 
= 39304

3. 78^3

Here, x = 7 and y = 8.
Using the formula, we have -
  7^3 | 3*7*7*8 | 3*7*8*8 | 8^3
= 343 | 1176 | 1344 | 512 
= 477552

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