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