Factoring the difference of two cubes.
a 3 + b 3 = (a + b)(a 2 " ab + b 2 )
a 3 " b 3 = (a " b)(a 2 + ab + b 2 )
Factor to find all real!solutions.
x 3 + 27
x 3 + 33
!
!
(x + 3)(x 2 " x(3) + 32 )
(x + 3)(x 2 " 3x + 9)
3
rewrite 27 as 3
factor using the given formula
!
!
simplify
!
(x 2 " 3x + 9) does not have any real solutions (b/c b 2 " 4ac < 0 ), so
!
!
!
!
(x + 3) = 0
Zero Product Property
x = "3
!
is the only real solution