Factor Polynomials

Question

Factor

2y^3-54z^3

Answer 1

First factor out a 2:

 

2(y³ - 27z³)

 

Now notice that this is the difference of two cubes -- y and 3z.

 

The standard factoring for the difference of 2 cubes is:L

 

a³ - b³ = (a - b)(a² + ab + b²)

 

In this case plug y in for a and 3z in for b:

 

2(y³ - 27z³) =

2(y - 3z)(y² + y(3z) + (3z)²) =

2(y - 3z)(y² + 3yz + 9z²)

 

 

Answer 2

2y³ - 54z³

2(y³ - 27z³)       This is in the form a difference of cubes. (a - b)(a² + ab + b²⁾

2(y - 3z)(y² + 3yz + 9z²)