a) \(ab+acbx=ab\left(1+cx\right)\)
b) \(ab-ac+ad=a\left(b-c+d\right)\)
c) \(ax-bx-cx+dx=x\left(a-b-x+d\right)\)
d) \(a\left(b+c\right)-d\left(b+c\right)=\left(b+c\right)\left(a-d\right)\)
e) \(ac-ad+bc-bd=a\left(c-d\right)+b\left(c-d\right)=\left(a+b\right)\left(c-d\right)\)
f) \(ax+by+bx+ay=\left(ax+bx\right)+\left(by+ay\right)\)
\(=x\left(a+b\right)+y\left(a+b\right)=\left(a+b\right)\left(x+y\right)\)