Question

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

Explanation:

Step1: Recognize difference of squares

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

Step2: Apply difference of squares formula

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

Step3: Factor remaining difference of squares

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

Answer:

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

Alternatively, if restricting to integer coefficients, the fully factored form over integers is:
$(5y^2 - 1)(5y^2 + 1)$