SOAP method

Question

Simplify 

 

x³+8

Answer 1

Using Same Opposite Always Positive (SOAP) to factor some special cubic expressions, the rule is:

 

   a³ ± b³ = (a [same sign] b) (a² [opposite sign] ab [always positive] b²)

 

For x³ + 2³        (you should memorize some cubes:2³, 3³, 4³, 5³, ...10³)

    same sign is   "+"

    opposite sign is    "-"

    a   is    x

    b   is    2

 

So,

  this simplifies to     (x+2)(x² -2x + 4)     answer

 

 

Can you factor x³ - 27   ??

Answer 2

x³ + 8

x³ + 2³

(x + 2)(x² - 2x + 4)