\(a,a\left(b+c\right)-d\left(b+c\right)\)

\(=\left(b+c\right)\left(a-d\right)\)

\(b,ac-ad+bc-bd\)

\(=a\left(c-d\right)+b\left(c-d\right)\)

\(=\left(a+b\right)\left(c-d\right)\)

\(c,ax+ay+bx+by\)

\(=\left(ax+bx\right)+\left(ay+by\right)\)

\(=x\left(a+b\right)+y\left(a+b\right)\)

\(=\left(x+y\right)\left(a+b\right)\)