or you can make the 81x81x81x81x80. It would be definitely shorter. I would use such things when the numbers are too big. That's why you're getting my thumb :)
Yikes! I just watched this, and I don't see how this is easier than calculating x = (81^2)^2, and then y = 81x, and then taking y - x. Even easier, calculate (81^2)^2 = (6561)^2 = 43046721 (just using standard multiplication), than multiplying by 80, which is simple since you just multiply by 8 and then add a zero to the end.
81^5 - 81^4 = 81^4 (81 - 1) Then 81 = 3^4, so 81^4 = (3^4)^4 = 3^16 and 80 = 2^4 * 5 so in terms of a prime factorization, the answer is: 2^4 * 3^16 * 5
Soluzione fantasiosa, ma eccessivamente lunga. Una volta che arrivi a 80x81^4 esegui i calcoli come insegnato alle scuole elementari: ci metti più o meno 5 minuti.
A very good solution. However, when adding the numbers one below the other, you added a zero to the penultimate one.
1:35 x=(81^4)80
81^4=(9^2)^4=9^8=(10-1)^8=
[1 -8 28 -56 70 -56 28 -8 1]
=100000000 - 80000000
+28000000 - 5600000
+ 700000 - 56000
+ 2800 - 80
+ 1 =
=128702801 - 85656080=
- 85656080
= 43046721
x=43046721•80=
=43046721(100-2•10)=
=4304672100
- 860934420=
=3443737680 😁
or you can make the 81x81x81x81x80. It would be definitely shorter. I would use such things when the numbers are too big. That's why you're getting my thumb :)
Yikes! I just watched this, and I don't see how this is easier than calculating x = (81^2)^2, and then y = 81x, and then taking y - x.
Even easier, calculate (81^2)^2 = (6561)^2 = 43046721 (just using standard multiplication), than multiplying by 80, which is simple since you just multiply by 8 and then add a zero to the end.
A bit of common sense is essential while solving these problems. Just because you know binomial theorem, don't apply it when not required.
one minor mistake, you were supposed to add on line 4, 37000 not 370000.
81^5 - 81^4
= 81^4 (81 - 1)
Then 81 = 3^4, so 81^4 = (3^4)^4 = 3^16
and 80 = 2^4 * 5
so in terms of a prime factorization, the answer is:
2^4 * 3^16 * 5
Quite right!
Perfect teaching
Too great
Good teaching skill
good for learning maam
Good
great solution maam
Nice solution
Soluzione fantasiosa, ma eccessivamente lunga. Una volta che arrivi a 80x81^4 esegui i calcoli come insegnato alle scuole elementari: ci metti più o meno 5 minuti.
Si fa prima a moltiplicare 81^4😂
80 · 81^4
🥱
Perfect example maam
Hint: 65^2 = 4225
[(6+1)×6] = 42
This is valid for numbers with 5 at unit place.
For example, 115^2..
12×11 = 132.
Then 115^2 = 13225.
All steps are correct
unfortunately not: the addition at the end isn't correct, because of one "0" too much!
81*81=6,561
6561(6561)=4,30,46,721
43046721*80=3,44,37,37,680