a) ax-bx+x+ay-by+y
= (a-b+1)x+(a-b+1)y
= (a-b+1)(x+y)
b) am+an+ap-bm-bn-bp-m-n-p
= a(m+n+p)-b(m+n+p)-(m+n+p)
= (a-b-1)(m+n+p)

a) \(ax-by+ay-bx=x\left(a-b\right)+y\left(a-b\right)=\left(a-b\right)\left(x+y\right)\)

b) \(am+bn+bm+an-m-n=m\left(a+b-1\right)+n\left(a+b-1\right)=\left(a+b-1\right)\left(m+n\right)\)

a) ax - by + ay - bx

= (ax+ay) - (bx + by)

= a (x+y) - b (x+y)

= (x+y) (a-b)

b) am + bn +bm + an - m - n

= (am + bm - m) + (bn +an -n)

=m (a +b - 1) + n (a + b - 1 )

= (m+n) ( a + b -1)

a/ \(ab-2b-3a+6=\left(ab-2b\right)-\left(3a-6\right)=b\left(a-2\right)-3\left(a-2\right)=\left(a-2\right)\left(b-3\right)\)

b/ \(ax-by-ay+bx==\left(ax+bx\right)-\left(by+ay\right)=x\left(a+b\right)-y\left(b+a\right)=\left(a+b\right)\left(x-y\right)\)

c/ \(ax+by-ay-bx=\left(ax-ay\right)+\left(by-bx\right)=a\left(x-y\right)+b\left(y-x\right)=a\left(x-y\right)-b\left(x-y\right)=\left(x-y\right)\left(a-b\right)\)

d/ \(a^2-\left(b+c\right)a+bc=a^2-ab-ac+bc=\left(a^2-ac\right)+\left(ab-bc\right)=a\left(a-c\right)+b\left(a-c\right)=\left(a-c\right)\left(a+b\right)\)e/ \(\left(3a-2\right)\left(4a-3\right)-\left(2-3a\right)\left(3a+1\right)=\left(3a-2\right)\left(4a-3\right)+\left(3a-2\right)\left(3a+1\right)=\left(3a-2\right)\left(4a-3+3a+1\right)=\left(3a-2\right)\left(7a-2\right)\)

f/ \(ax+ay+az-bx-by-bz-x-y-z=\left(ax+ay+az\right)-\left(bx+by+bz\right)-\left(x+y+z\right)\)

\(=a\left(x+y+z\right)-b\left(x+y+z\right)-\left(x+y+z\right)=\left(x+y+z\right)\left(a-b-1\right)\)