Difference between revisions of "2021 AMC 12A Problems/Problem 9"
Pi is 3.14 (talk | contribs) (→Video Solution by Hawk Math) |
Pi is 3.14 (talk | contribs) (→Video Solution by pi_is_3.14(Factorizations/Telescoping& Meta-solving)) |
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https://youtu.be/H34IFMlq7Lk | https://youtu.be/H34IFMlq7Lk | ||
Revision as of 23:18, 11 February 2021
Contents
Problem
Which of the following is equivalent to
![\[(2+3)(2^2+3^2)(2^4+3^4)(2^8+3^8)(2^{16}+3^{16})(2^{32}+3^{32})(2^{64}+3^{64})?\]](http://latex.artofproblemsolving.com/6/5/a/65a7155ec29794e20977d4bf1eef21987af9bbee.png)
Solution 1
All you need to do is multiply the entire equation by 
. Then all the terms will easily simplify by difference of squares and you will get 
or 
as your final answer. Notice you don't need to worry about 
because that's equal to 
.
-Lemonie
Video Solution by Hawk Math
https://www.youtube.com/watch?v=P5al76DxyHY
Video Solution by OmegaLearn(Factorizations/Telescoping& Meta-solving)
~ pi_is_3.14
See also
| 2021 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 8 |
Followed by Problem 10 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
| 2021 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.
