Answer:
![m^2 +1](https://tex.z-dn.net/?f=m%5E2%20%2B1)
Explanation:
All the other expressions can be factorized. Let's see why:
1) ![m^3 +1](https://tex.z-dn.net/?f=m%5E3%20%2B1)
This is the sum of the cubes, and this can be factorized as follows:
![a^3+b^3=(a+b)(a^2-ab+b^2)](https://tex.z-dn.net/?f=a%5E3%2Bb%5E3%3D%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29)
In this case, a=m and b=1, so we can factorize as
![m^3+1=(m+1)(m^2-m+1)](https://tex.z-dn.net/?f=m%5E3%2B1%3D%28m%2B1%29%28m%5E2-m%2B1%29)
2) ![m^3-1](https://tex.z-dn.net/?f=m%5E3-1)
This is the difference between two cubes, and this can be factorized as follows:
![a^3-b^3=(a-b)(a^2+ab+b^2)](https://tex.z-dn.net/?f=a%5E3-b%5E3%3D%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29)
In this case, a=m and b=1, so we can factorize as
![m^3-1=(m-1)(m^2+m+1)](https://tex.z-dn.net/?f=m%5E3-1%3D%28m-1%29%28m%5E2%2Bm%2B1%29)
3) ![m^2-1](https://tex.z-dn.net/?f=m%5E2-1)
This is the difference between two square numbers, and it can be factorized as follows
![(a^2-b^2)=(a+b)(a-b)](https://tex.z-dn.net/?f=%28a%5E2-b%5E2%29%3D%28a%2Bb%29%28a-b%29)
In this case, a=m and b=1, so we can factorize as
![m^2-1=(m+1)(m-1)](https://tex.z-dn.net/?f=m%5E2-1%3D%28m%2B1%29%28m-1%29)
Equivealent= like
6/18, 5/15
3/9, 2/6
Answer:
64+24
Step-by-step explanation:
Answer:
![128 \pi/5 units^3](https://tex.z-dn.net/?f=128%20%5Cpi%2F5%20units%5E3)
Step-by-step explanation:
The volume of the solid revolution is expressed as;
![V = \int\limits^2_0 {\pi y^2} \, dx](https://tex.z-dn.net/?f=V%20%3D%20%5Cint%5Climits%5E2_0%20%7B%5Cpi%20y%5E2%7D%20%5C%2C%20dx)
Given y = 2x²
y² = (2x²)²
y² = 4x⁴
Substitute into the formula
![V = \int\limits^2_0 {4\pi x^4} \, dx\\V =4\pi \int\limits^2_0 { x^4} \, dx\\V = 4 \pi [\frac{x^5}{5} ]\\](https://tex.z-dn.net/?f=V%20%3D%20%5Cint%5Climits%5E2_0%20%7B4%5Cpi%20x%5E4%7D%20%5C%2C%20dx%5C%5CV%20%3D4%5Cpi%20%5Cint%5Climits%5E2_0%20%7B%20x%5E4%7D%20%5C%2C%20dx%5C%5CV%20%3D%204%20%5Cpi%20%5B%5Cfrac%7Bx%5E5%7D%7B5%7D%20%5D%5C%5C)
Substituting the limits
![V = 4 \pi ([\frac{2^5}{5}] - [\frac{0^5}{5}])\\V = 4 \pi ([\frac{32}{5}] - 0)\\V = 128 \pi/5 units^3](https://tex.z-dn.net/?f=V%20%3D%204%20%5Cpi%20%28%5B%5Cfrac%7B2%5E5%7D%7B5%7D%5D%20-%20%5B%5Cfrac%7B0%5E5%7D%7B5%7D%5D%29%5C%5CV%20%3D%204%20%5Cpi%20%28%5B%5Cfrac%7B32%7D%7B5%7D%5D%20-%200%29%5C%5CV%20%3D%20128%20%5Cpi%2F5%20units%5E3)
Hence the volume of the solid is ![128 \pi/5 units^3](https://tex.z-dn.net/?f=128%20%5Cpi%2F5%20units%5E3)