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# factor the expression x^6-1, using the following methods

Factor the expression x^6-1, using the following methods (a)Factor the expression by treating it as the difference of two squares, (x^3)^2-1^2 (b) Factor the expression, treating it as the difference of two cubes, (x^2)^3-1^3

### 2 Answers by Expert Tutors

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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a)
x^6 - 1
= (x^3)^2 - 1
= (x^3 + 1)(x^3 - 1)
= (x+1)(x^2 - x + 1)(x-1)(x^2 + x +1)
= (x+1)(x-1)(x^2 - x +1)(x^2 + x + 1)

b)
x^6 - 1
= (x^2)^3 - 1
= (x^2 - 1)(x^4 + x^2 + 1)
= (x+1)(x-1)(x^4+2x^2+1 - x^2)
= (x+1)(x-1)[(x^2+1)^2 - x^2)
= (x+1)(x-1)(x^2-x+1)(x^2+x+1)

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
0
Have to use identity

X - Y = ( X - Y ) ( X +Y )!
X- Y = ( X - Y ) ( X+ xy + y2  )

FIRST  : (x 6  - 1 ) = ( x+ 1 ) ( x3 + 1 ) = ( x + 1 ) ( x2 - x + 1 ) ( x -1) ( x2 + x + 1 )