How do you factor #x^2-y^2-x+y#?

Question

4531 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-24T16:43:41

#(x-y)(x+y-1)#

#"Apply "a^2-b^2=(a-b)(a+b)#

#=> x^2-y^2-x+y = (x-y)(x+y)-x+y#

#"(now separate "(x-y)")"#

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

Answer 2 · 2018-04-24T17:16:21

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

Factorise by grouping the four terms into pairs first.

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

Factorise the difference of squares.

#=(x+y)(x-y) color(blue)(-(x-y))" "larr# note the change of signs

NOw there is a common bracket in the two terms:

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