Question

Factor completely x8 − 81. (x4 − 9)(x4 9) (x2 − 3)(x2 3)(x4 − 9) (x2 − 3)(x2 3)(x4 9) (x2 − 3)(x2 − 3)(x4 − 9).

Answer 1

Answer:B

Explanation:

(x2 − 3)(x2 + 3)(x4 + 9)

Answer 2

(x² - 3)(x² + 3)(
`x^(4)` + 9)

Explanation:

`x^(8)` - 81 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

`x^(8)` - 81

= (
`x^(4)` )² - 9²

= (
`x^(4)` - 9)(
`x^(4)` + 9) ←
`x^(4)` - 9 is also a difference of squares

= (x² - 3)(x² + 3)(
`x^(4)` + 9)