Factoring

[Asian]

How would you factor:

 

A^3 + B^3 + A^2 - B^2

[CPL.Luke]

set it equal to zero and solve (if by hand look up and use cardano's method)

 

then plug the roots into the expression (A-a1)(A-a2)(A-a3)

 

where a1,a2,a3 are the roots and should be functions of B

 

^note in the above your using A as your x.

[Cap'n Refsmmat]

[math]a^3 + b^3 + a^2 - b^2[/math]

Hmm... break it up into a difference of two squares and a sum of two cubes:

[math](a + b)(a^2 - ab + b^2) + (a + b)(a - b)[/math]

 

I think it can be simplified further from there, but I won't do the rest of your work for you.

 

 

edit: I seem to be outclassed.

[Asian]

so then the rest is factor by grouping........ thanks, i just wanted to check my answer because it wasnt in the back of the book and i have a test tomorrow.

[CPL.Luke]

not outclassed, I can't spot tricks like that for anything so I just figure out ways of guaranteeing an answer no matter what the polynomial is.