Question

URGENT!
Factor completely x^8 − 625.
(x4 − 25)(x4 + 25)
(x2 − 5)(x2 + 5)(x4 − 25)
(x2 − 5)(x2 − 5)(x4 − 25)
(x2 − 5)(x2 + 5)(x4 + 25)

Answer 1

Answer:

(x² - 5)(x² + 5)(x⁴ + 25)

Step-by-step explanation:

$x^8-625=x^{4\cdot2}-25^2\qquad\text{use}\ (a^n)^m=a^{n\cdot m}\qquad(*)\\\\=(x^4)^2-25^2\qquad\text{use}\ a^2-b^2=(a+b)(a-b)\qquad(**)\\\\=(x^4+25)(x^4-25)=(x^4+25)(x^{2\cdot2}-5^2)\qquad\text{use}\ (*)\\\\=(x^4+25)\bigg((x^2)^2-5^2\bigg)\qquad\text{use}\ (**)\\\\=(x^4+25)(x^2+5)(x^2-5)$