How do you factor 27 - x^12?

It's a perfect cube, right? Please explain.

Todd2011-09-19T13:18:22Z

Favorite Answer

Yes, it's a difference of cubes.

27 = 3^3
x^12 = (x^4)^3.

The general equation is (a-b)^3 = (a-b) * (a^2 + ab + b^2). Thus, we get

(3-x^4) * (9 + 3x^4 + x^8).

?2011-09-19T20:19:29Z

Difference of cubes: 27 = 3^3, x^12 = (x^4)^3

27 - x^12 = (3 - x^4) (9 + 3x^4 + x^8)

-- Ματπmφm --

David2011-09-19T20:16:16Z

27 - x^12

(3 - x^4)(9 + 3x^4 + x^8)

Guillermo2011-09-19T20:14:23Z

- (x^4 - 3)*(x^8 + 3*x^4 + 9)

?2011-09-19T20:22:01Z

27 - X¹² = 3³ - (x⁴)³

= (3 - x⁴)[(x⁴)² + 3x⁴ + 3²]

= (3 - x⁴)(x⁸ + 3x⁴ + 9)