Factoring (Again)

Question

How do I factor y³-8?

Answer 1

Taylor,

Just like factoring the difference of squares has a consistent format... a^2- b^2 = (a-b)(a+b), the factors of a difference of cubes also has a pattern... a^3-b^3= (a-b)(a^2+ab+b^2)

In your example the y is obviously cubed and 8 is the same as 2^3.  I hope this helps.

Answer 2

y³ - 8   is the difference of two cubes:    y³ - 2³

      You may see the difference of squares and the difference of cubes in lots of problems.

 

The formula is:

    a³ - b³  =  (a - b)(a² + ab + b²)              [multiply it out, then memorize it]

 

For this problem:

    y³ - 2³  = (y - 2)(y² + 2y + 4)                [remember, 2² = 4]