Question

factorise x^2-y^2-x-y

Answer 1

x²-y²-x-y=0

(x²-y²)-(x+y)=0

we know that a²-b²=(a+b)(a-b)

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

taking (x+y) as common

(x+y)((x-y)-1)=0
we get 2 equations and equate into zero

x+y=0---->1
x-y-1=0
x-y=1----->2
by solving equation 1 & equation 2


x+y=0
x-y=1
----------
2x=1
x=1/2

substitute X=1/2 in equation 1
x+y=0
1/2+y=0
y=-1/2


therefore
the value of X= 1/2;
the value of Y= -1/2.