2007-05-21 13:52:18 · 5 answers · asked by pkbrauer 1 in Science & Mathematics ➔ Mathematics
Difference of squares:
x^8 - 25 =
(x^4 + 5)(x^4 - 5)
You could factor that second term further, using the same rule:
(x^4 + 5)(x^4 - 5) =
(x^4 + 5)(x^2 + sqrt(5))(x^2 - sqrt(5))
And you could factor that final term further, again:
(x^4 + 5)(x^2 + sqrt(5))(x^2 - sqrt(5))
(x^4 + 5)(x^2 + sqrt(5))(x + sqrt(sqrt(5)))(x - sqrt(sqrt(5)))
... but factoring down to the fourth root of 5 is maybe overkill.
2007-05-21 14:05:08 · answer #1 · answered by McFate 7 · 0⤊ 0⤋
(x^4 + 5)(x^4 - 5)
2007-05-21 13:55:23 · answer #2 · answered by Ana 4 · 0⤊ 0⤋
its a perfect square
(x^4-5)(x^4+5)
when its a perfect square you have the same numbers just different signs so the middle terms cancels out:)
2007-05-21 13:59:55 · answer #3 · answered by :) 5 · 0⤊ 0⤋
(x^4+5)(x^4-5)
2007-05-21 13:55:20 · answer #4 · answered by Austin 2 · 0⤊ 1⤋
(x^4+5)(x^2+sqrt(5) )(x+ 4th root(5) )(x-4th root(5) )
2007-05-21 14:09:36 · answer #5 · answered by sothanaphan 2 · 0⤊ 0⤋