(x^2 + x + y - y^2) PLEASE FACTOR AND EXPLAIN?

Question

please.. i know the answer but i know how he got it

Answer 1

= x² + x + y - y²

= (x + y)(x - y + 1)

Answer: (x + y)(x - y + 1)

Checking by F.O.I.L.

= (x + y)(x - y + 1)

= x² - xy + x + xy - y² + y

= x² + x - y² + y rearrange to original expression

= x² + x + y - y²

Answer 2

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

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

write  x^2 - y^2  as (x - y)(x + y)

[(x - y)(x + y) + (x + y).1]

(x + y)(x - y  + 1)

Answer 3

(x^2+x+y-y^2)=0

then combine like terms

(x^2+x)+(y-y^2)=0

x(x+1)+y(1-y)=0 since 1 is common on both terms you can just simply put 1 then combine the terms

(x+y)[(x+1-y)]=0 this is the simplest form but if you want to be sure you can recheck it by multiplying the terms:

(x+y)[(x+1-y)]=0

x^2+x-xy+yx+y-y^2=0 cancelling -xy and yx

x^2+x+y-y^2=0