Difference between revisions of "2000 SMT/Algebra Problems/Problem 2"
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| − | Problem 2 | + | ==Problem 2== |
| − | Evaluate 2000^3 - 1999(2000^2) - 1999^2(2000) + 1999^3 | + | Evaluate <math>2000^3 - 1999(2000^2) - 1999^2(2000) + 1999^3</math> |
| − | Solution 1 - | + | ==Solution 1 - Submitted by howdoi_yt== |
| − | I can | + | I can rewrite the first <math>1999</math> as <math>(2000-1)</math>, and the third <math>2000</math> as <math>(1999+1)</math>; |
| − | 2000^3 - 2000^2(2000-1) - 1999^2(1999+1) + 1999^3 = 2000^3 - 2000^3 + 2000^2 - 1999^3 - 1999^2 + 1999^3 = 2000^2 - 1999^2 = (2000 - 1999)(2000 + 1999) = | + | |
| − | + | <math>2000^3 - 2000^2(2000-1) - 1999^2(1999+1) + 1999^3</math> | |
| + | |||
| + | <math>= 2000^3 - 2000^3 + 2000^2 - 1999^3 - 1999^2 + 1999^3</math> | ||
| + | |||
| + | <math>= 2000^2 - 1999^2</math> | ||
| + | |||
| + | <math>= (2000 - 1999)(2000 + 1999)</math> | ||
| + | |||
| + | <math>= 3999 \qquad \blacksquare</math> | ||
Latest revision as of 14:14, 18 April 2023
Problem 2
Evaluate 
Solution 1 - Submitted by howdoi_yt
I can rewrite the first 
as 
, and the third 
as 
;
