what is x to the third power - 27

Question

x³-27 factor the sum or difference of cubes

Answer 1

x^3-27

=(x-3)(x^2+3x+9)

 

 

x^3+27

=(x+3)(x^2-3x+9)

Answer 2

The formula for the difference of perfect cubes is x^3 -  a^3 = (x-a)(x^2 + ax + a^2). So your expression can be written 

x^3 - 3^3 making a=3. Substituting into the formula you get (x-3)(x^2 + 3x + 9).

Answer 3

x³  = -27

then x = ³√(-27) = -3

 

To factor, you can use formula,  

              x³ + y³ = (x + y)(x² - xy + y²)

              x³ - y³ = (x - y)(x² + xy + y²)

 

x³ -27 =  x³ + (-3)³  = (x+ (-3))(x² - x(-3) + (-3)²)

          =  (x - 3)(x² + 3x + 9)