* ax+bx+ay+by=x.(a+b)+y.(a+b)=(x+y).(a+b)

* x³-x²+x-1=x².(x-1)+(x-1)=(x-1).(x²+1)

* xy-4x-4y+16= x(y-4)-4(y-4) = (y-4).(x-4)

*

a²-ba-a+b

a-1

=

a(a-b)-(a-b)

a-1

=a-b

*

4ab-2a-2b²+b

2a-b

=

2a(2b-1)-b(2b-1)

a-1

=

(2b-1).(2a-b)

2a-b

=2b-1

*

3ab-3xb+xy-ay

x-a

=

3b(a-x)-y(a-x)

x-a

=

(a-x).(3b-y)

x-a

=

(x-a).(y-3b)

x-a

=y-3b

.