Trick of the Day - Subtracting Adjacent Cubes

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Trick of the Day - Subtracting Adjacent Cubes

Post by Ani on Tue Mar 03, 2009 7:13 pm

Ok, this trick is for when you are asked to subtract two cubes in which one is one more than the other.

ex. 1 - 25^3-24^3
1. The trick is 1 + 3ab where a is one number and b is the other.
2. 1 + 3(25)(24) = 1801

This is because x^3 - y^3 = (x-y)(x^2 +xy + y^2) = (x-y)((x-y)^3 + 3xy)
and since x = y + 1,
(1)(1^3 + 3xy) = 1 + 3xy

Practice!!!!!!!!!!!!!!!!!!!
1. 10^3 - 9^3
2. 19^3 - 18^3
3. 51^3 - 50^3
4. 61^3 - 60^3
5. 31^3 - 30^3
6. 101^3 - 100^3
7. 56^3 - 55^3
8. 75^3 - 74^3
9. 50^3 - 49^3
10. 26^3 - 25^3
11. 41^3 - 40^3
12. 100^3 - 99^3
13. 3001^3 - 3000^3
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