Answer:
my answer is in this picture
Start by laying out the 12.
The neighbors of 12 must be 11 and 10.
The neighbor of 11 must be 9, and the neighbor of 10 must be 8, and so on and so forth, until you get a unique arrangement.
False, It was till Pack 5 it was going up 3 every pack but at 5 it went up 13 cookies.
Answer:
The factorization of
is ![(9x^{5} +10)(81x^{10} -90x^{5} +100)](https://tex.z-dn.net/?f=%289x%5E%7B5%7D%20%2B10%29%2881x%5E%7B10%7D%20-90x%5E%7B5%7D%20%2B100%29)
Step-by-step explanation:
This is a case of factorization by <em>sum and difference of cubes</em>, this type of factorization applies only in binomials of the form
or
. It is easy to recognize because the coefficients of the terms are <u><em>perfect cube numbers</em></u> (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).
Let's solve the factorization of
by using the <em>sum and difference of cubes </em>factorization.
1.) We calculate the cubic root of each term in the equation
, and the exponent of the letter x is divided by 3.
![\sqrt[3]{729x^{15}} =9x^{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B729x%5E%7B15%7D%7D%20%3D9x%5E%7B5%7D)
then ![\sqrt[3]{10^{3}} =10](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B10%5E%7B3%7D%7D%20%3D10)
So, we got that
which has the form of
which means is a <em>sum of cubes.</em>
<em>Sum of cubes</em>
![(a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})](https://tex.z-dn.net/?f=%28a%5E%7B3%7D%20%2Bb%5E%7B3%7D%20%29%3D%28a%2Bb%29%28a%5E%7B2%7D%20-ab%2Bb%5E%7B2%7D%29)
with
y ![b=10](https://tex.z-dn.net/?f=b%3D10)
2.) Solving the sum of cubes.
![(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )](https://tex.z-dn.net/?f=%289x%5E%7B5%7D%29%5E%7B3%7D%20%2B%20%2810%29%5E%7B3%7D%3D%289x%5E%7B5%7D%20%2B10%29%28%289x%5E%7B5%7D%29%5E%7B2%7D-%289x%5E%7B5%7D%29%2810%29%2B10%5E%7B2%7D%20%29)
![(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)](https://tex.z-dn.net/?f=%289x%5E%7B5%7D%29%5E%7B3%7D%20%2B%20%2810%29%5E%7B3%7D%3D%289x%5E%7B5%7D%20%2B10%29%2881x%5E%7B10%7D-90x%5E%7B5%7D%2B100%29)
.