Difference between revisions of "2000 SMT/Algebra Problems/Problem 2"
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Evaluate <math>2000^3 - 1999(2000^2) - 1999^2(2000) + 1999^3</math> | Evaluate <math>2000^3 - 1999(2000^2) - 1999^2(2000) + 1999^3</math> | ||
| − | ==Solution 1 - | + | ==Solution 1 - Submitted by howdoi_yt== |
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| + | I can rewrite the first <math>1999</math> as <math>(2000-1)</math>, and the third <math>2000</math> as <math>(1999+1)</math>; | ||
| − | |||
<math>2000^3 - 2000^2(2000-1) - 1999^2(1999+1) + 1999^3</math> | <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>= 2000^3 - 2000^3 + 2000^2 - 1999^3 - 1999^2 + 1999^3</math> | ||
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<math>= 2000^2 - 1999^2</math> | <math>= 2000^2 - 1999^2</math> | ||
| + | |||
<math>= (2000 - 1999)(2000 + 1999)</math> | <math>= (2000 - 1999)(2000 + 1999)</math> | ||
| − | <math>= 3999 \blacksquare</math> | + | |
| + | <math>= 3999 \qquad \blacksquare</math> | ||
Latest revision as of 15:14, 18 April 2023
Problem 2
Evaluate 
Solution 1 - Submitted by howdoi_yt
I can rewrite the first 
as 
, and the third 
as 
;
