2021 AMC 12A Problems/Problem 9
Revision as of 18:20, 11 February 2021 by Pi is 3.14 (talk | contribs) (→Video Solution by Hawk Math)
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 pi_is_3.14(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 | |
The problems on this page are copyrighted by the Mathematical Association of America's 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
