Identify the factors of x2 + 16y2.
1 answer:
Answer:
The correct option is C.
Step-by-step explanation:
The given expression is
![x^2+16y^2](https://tex.z-dn.net/?f=x%5E2%2B16y%5E2)
In option A,
![(x+4y)(x+4y)=x^2+4xy+4xy+16y^2=x^2+8xy+16y^2](https://tex.z-dn.net/?f=%28x%2B4y%29%28x%2B4y%29%3Dx%5E2%2B4xy%2B4xy%2B16y%5E2%3Dx%5E2%2B8xy%2B16y%5E2)
Therefore option A is incorrect.
In option B,
![(x+4y)(x-4y)=x^2-4xy+4xy-16y^2=x^2-16y^2](https://tex.z-dn.net/?f=%28x%2B4y%29%28x-4y%29%3Dx%5E2-4xy%2B4xy-16y%5E2%3Dx%5E2-16y%5E2)
Therefore option B is incorrect.
In option D,
![(x-4y)(x-4y)=x^2-4xy-4xy-16y^2=x^2-8xy+16y^2](https://tex.z-dn.net/?f=%28x-4y%29%28x-4y%29%3Dx%5E2-4xy-4xy-16y%5E2%3Dx%5E2-8xy%2B16y%5E2)
Therefore option D is incorrect.
Since the given expression can not be factored further, therefore it is a prime expression and option C is correct.
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