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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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