Math Simplify Problem

Question

How can i simplify x^4 - 2xy - y^2 + 2x^3 . i have tried maybe over 100 times i used the apps for math solving they didnt help . Can this be simplified because the teacher gave this to us

Answer 1

I spotted the terms x^4 - y^2 as the difference of two squares.

Factor that, then see if you can regroup and find a new common factor.

It turns out that you can.

 

Regroup:

(x^4 - y^2) + (2x^3 - 2xy)

Factor

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

There is now a common factor in these two terms:

(x^2-y) [(x^2+y) + 2x]

Simplify a little more:

(x^2-y) (x^2+2x+y]

 

I don't see any more opportunities for further simplification.

Answer 2

x^4-2xy-y^2+2x^3

this can be written as a product if you want to consider this simplified

x^4-y^2-2xy+2x^3

(x^4-y^2)+(-2xy+2x^3)

factor

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

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

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