How do I factorise this cubic expression?

[physicsfun_12]

Homework Statement

Hello there, hope you'r well.

I am having trouble factorising this cubic. I am comfortable with quadratics however I have never had to factorise anything to the power 3 before.

x^3+3x^2y+2xy^2+6y^3

Thanks in advance for any input.

Mike

Homework Equations

n/a

The Attempt at a Solution

I have had ago but didn't get very far!

(3x+2y)(xy) that does the bit in the middle, excluding the two terms to the power 3.

Thanks again for any help with this.

Mike

 

[tiny-tim]

x^3+3x^2y+2xy^2+6y^3

Hi Mike!

(try using the X² tag just above the Reply box )

Assuming it has rational roots, they must be x/y = ± 1 or 2 or 3 or 6, so just try all of them.

(to save time, do the "odd" terms together, and the "even" terms together )

 

[LCKurtz]

Try grouping the first two and last two terms together and factor each group. Then...

 

[VeeEight]

Factor x² from the first two terms and 2y² from the last two terms.