Question

question
factor completely.
$25z^4 - 1$

Explanation:

Step1: Recognize difference of squares

$25x^4 - 1 = (5x^2)^2 - (1)^2$

Step2: Apply difference of squares formula

$(5x^2 - 1)(5x^2 + 1)$

Step3: Factor remaining difference of squares

$5x^2 - 1 = (\sqrt{5}x)^2 - (1)^2 = (\sqrt{5}x - 1)(\sqrt{5}x + 1)$

Answer:

$(\sqrt{5}x - 1)(\sqrt{5}x + 1)(5x^2 + 1)$

Alternatively, if restricting to integer coefficients, the fully factored form with integer terms is $(5x^2 - 1)(5x^2 + 1)$. For complete real factorization, the answer above with linear terms is correct.