Problem: The factors of x4+64x^{4}+64x4+64 are:
Answer Choices:
A. (x2+8)2\left(x^{2}+8\right)^{2}(x2+8)2
B. (x2+8)(x2−8)\left(x^{2}+8\right)\left(x^{2}-8\right)(x2+8)(x2−8)
C. (x2+2x+4)(x2−8x+16)\left(x^{2}+2 x+4\right)\left(x^{2}-8 x+16\right)(x2+2x+4)(x2−8x+16)
D. (x2−4x+8)(x2−4x−8)\left(x^{2}-4 x+8\right)\left(x^{2}-4 x-8\right)(x2−4x+8)(x2−4x−8)
E. (x2−4x+8)(x2+4x+8)\left(x^{2}-4 x+8\right)\left(x^{2}+4 x+8\right)(x2−4x+8)(x2+4x+8) Solution:
x4+64=(x4+16x2+64)−16x2x^{4}+64=\left(x^{4}+16 x^{2}+64\right)-16 x^{2} x4+64=(x4+16x2+64)−16x2
=(x2+8)2−(4x)2=(x2+4x+8)(x2−4x+8)=\left(x^{2}+8\right)^{2}-(4 x)^{2}=\left(x^{2}+4 x+8\right)\left(x^{2}-4 x+8\right) =(x2+8)2−(4x)2=(x2+4x+8)(x2−4x+8)