a) \(x^2-x-y^2-y\)
\(=\left(x^2-y^2\right)-\left(x+y\right)\)
\(=\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-1\right)\)
b) \(x^2-2xy+y^2-z^2\)
\(=\left(x^2-2xy+y^2\right)-z^2\)
\(=\left(x-y\right)^2-z^2\)
\(=\left(x-y-z\right)\left(x-y+z\right)\)
c) \(5x-5y+ax-ay\)
\(=\left(5x-5y\right)+\left(ax-ay\right)\)
\(=5\left(x-y\right)+a\left(x-y\right)\)
\(=\left(x-y\right)\left(5+a\right)\)
A) x2 - x- y2 - y
=(x2-y2)-(x+y)
=(x-y)(x+y)-(x+y)
=(x+y)(x-y-1)
B) x2 - 2xy + y2 - z2
= (x2-2xy+y2)-z2
=(x-y)2-z2
=(x-y+z)(x-y-z)
C) 5x - 5y + ax - ay
= (5x-5y)+(ax-ay)
=5(x-y)+a(x-y)
= (x-y)(5+a)