Question

xy² + (x -1) y -1 factorization ​

Answer 1

Answer:

I'm going to work with numerator and denominator separately.

For the numerator factor by grouping (A good thing to check when you got 4 terms)

x^3 - x^2 y + x^2 y^2 - y^3 can be broken into parts like this:

(x^3 - x^2 y) + (x^2 y^2 - y^3) factor out GCF for each group

x^2(x-y) + y^2(x-y) Now factor out the common (x-y)

(x-y)(x^2 + y^2) *Factored completely.

For the denominator: use sum of cubes x^3 + y^3 = (x+y)(x^2-xy+y^2)

x^6 + y^6 can be rewritten as (x^2)^3 + (y^2)^3 so now you can use the sum of cubes.

(x^2 + y^2) (x^4 - x^2 y^2 + y^4) *Completely factored

putting it together:

numerator: (x-y)(x^2 + y^2)

denominator: (x^2 + y^2) (x^4 - x^2 y^2 + y^4)

since (x^2 + y^2) is common to both, I can cancel them out to get

(x-y) / (x^4 - x^2 y^2 + y^4)

Enjoy!