Answer:
Answer: Third option is the right answer.
Step-by-step explanation:
First we the write the expression
![(a+b)(a^{2}+b^{2}-ab)](https://tex.z-dn.net/?f=%28a%2Bb%29%28a%5E%7B2%7D%2Bb%5E%7B2%7D-ab%29)
Now teacher says that the product of these polynomials will result in the sum of ![a^{3}+b^{3}](https://tex.z-dn.net/?f=a%5E%7B3%7D%2Bb%5E%7B3%7D)
Now the teacher ask if we put the value of a = 2x and b = 1 then what will be the expression look like.
![(2x+1)\left [ (2x)^{2}+(1^{2})-(2x)(1)\right ]](https://tex.z-dn.net/?f=%282x%2B1%29%5Cleft%20%5B%20%282x%29%5E%7B2%7D%2B%281%5E%7B2%7D%29-%282x%29%281%29%5Cright%20%5D)
=![(2x+1)(4x^{2}+1-2x)](https://tex.z-dn.net/?f=%282x%2B1%29%284x%5E%7B2%7D%2B1-2x%29)
So third option is looking like our expression.
Answer:16384
Step-by-step explanation:
4*4*4*4+4*4*4
Answer:
b. ![\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20225y%5E2%20%2B%20150xy%20%2B%20100x%5E2%20%3D%20225y%5E2%20%2B%20150xy%20%2B%20100x%5E2)
a. ![\displaystyle [8x + 12y]^2 + [6x + 9y]^2 = [10x + 15y]^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5B8x%20%2B%2012y%5D%5E2%20%2B%20%5B6x%20%2B%209y%5D%5E2%20%3D%20%5B10x%20%2B%2015y%5D%5E2)
Step-by-step explanation:
b. ![\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20225y%5E2%20%2B%20150xy%20%2B%20100x%5E2%20%3D%20225y%5E2%20%2B%20150xy%20%2B%20100x%5E2)
a. ![\displaystyle [8x + 12y]^2 + [6x + 9y]^2 = [10x + 15y]^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5B8x%20%2B%2012y%5D%5E2%20%2B%20%5B6x%20%2B%209y%5D%5E2%20%3D%20%5B10x%20%2B%2015y%5D%5E2)
The two expressions are identical on each side of the equivalence symbol, therefore they are an identity.
I am joyous to assist you anytime.
the last one because 7*3=21 14*3=42 and 21*3=63