Answer:
The factorization of
is 
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>

with
y 
2.) Solving the sum of cubes.


.
For finding the value of b, we must consider that Line MN passes through points M(4, 3) and N(7, 12). With this condition y = mx + b, can be written 3=4m+ b (because line passes through M(4,3) ) and 12=7m+b, b ( because line passes through M(7,12)).
We have a system of equation
4m+ b=3
7m+b=12
For solving this, 4m+b- (7m+b)= 3-12, it is equivalent to -3m= -9 and then m=3, if m=3 so
4x3 +b =3 implies b= 3 -12= -9, so the value of b= -9
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No -- other factors will influence whether your happy or not. Saying that is true is inductive reasoning, which is prone to error
Answer:
1/27 cubic in.
Step-by-step explanation:
1/3*1/3*1/3= 1/27
20 times 1/8+1/8+1/8+1/8+1/8=5/8 times 4 because of the four pots = 20