In the previous tutorial on mathematical shortcut, you learnt how easy it is to obtain the square of any number by slightly modifying the formula.As an extension to that shortcut, In this tutorial, we are going to learn how to obtain the cube of a number.

Once you practice this shortcut, you will see, how easy it is to obtain the cube of any 2-digit number and even some 3-digit numbers. In competitive examinations, we might have often come across questions like 97^{3}, 87^{3} etc.

In order to use this shortcut, is important that you know the cubes of all the numbers till 10 at least.

Let us recall the cubes of the number till 12.

Number |
Cube |

1 | 1 |

2 | 8 |

3 | 27 |

4 | 64 |

5 | 125 |

6 | 216 |

7 | 343 |

8 | 512 |

9 | 729 |

10 | 1000 |

11 | 1331 |

12 | 1728 |

I hope you all remember the square formula : ( a + b)^{3} = a^{3} + 3ab(a + b) + b^{3}

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

Lets modify the formula to look something like this :

Letâ€™s understand the shortcut with an example.

**Example :** Compute 14^{3}

**Step 1 : ** Break the number such that a=1, and b=4

**Step 2 : ** Compute a^{3}, a^{2}b and ab^{2} and write as shown in the updated formula

**Step 3 : **Notice the second row of the formula is obtained by doubling the middle 2-terms of the first row.

**Step 4 : **Add the terms. Notice the carry-forward in each step.

Very easy right đŸ™‚

**Example :** Letâ€™s take another example. Letâ€™s say we want to compute 52^{3}. In this a=5 and b=2.

** **

**Example :** Can you try what is 122^{3} ?

If you know the cubes of number till 10, you can easily obtain the cubes of all the numbers till 100 using this shortcut.

**Exercise :** On the similar lines, can you calculate,

- 15
^{3} - 34
^{3} - 67
^{3} - 99
^{3} - 105
^{3}

Please contact me if some point in the tutorial is not clear. I would be glad to help.

Hats off to ur trick sir.

very nicee……., shortcut key

Hey thank you so much… for giving suxh a nic shortcut tricks.. but i have prblm… i understood ur tricks… but i confused… sumtimes while finding main final ans could you pls elaborate me… asap