SOLUTION: How do I factor this equation? 256w^16 -v^16

Question 902232: How do I factor this equation?
256w^16 -v^16
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
How do I factor this equation?
It is an expression not an equation.
Equations equate with "=."
256w^16 -v^16
(16w^8-v^8)*(16w^8+v^8)
(16w^8-v^8) can be factored again
(4w^4-v^4)*(4w^4+v^4)
(4w^4+v^4) can be factored again
(v^2-2 v w+2 w^2) (v^2+2 v w+2 w^2)
(4w^4-v^4) can be factored again
(2w^2-v^2)*(2w^2+v^2)
Some say that (2w^2-v^2) can be factored again
(Sqrt(2)*w-v)*(Sqrt(2)*w+v)
so we have
256w^16 -v^16=
(Sqrt(2)*x-v)*(Sqrt(2)*x+v)*(v^2-2vw+2w^2)*(v^2+2vw+2w^2)*(2w^2+v^2)*(16w^8+v^8)
or more conservatively
256w^16 -v^16=
(2w^2-v^2) (v^2+2w^2) (v^2-2vw+2w^2) (v^2+2vw+2w^2) (16w^8+v^8)

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