\(a.a\left(b+c\right)+3b+3c=a\left(b+c\right)+3\left(b+c\right)=\left(b+c\right)\left(a+3\right)\)

\(b.a\left(c-d\right)+c-d=\left(c-d\right)\left(a+1\right)\)

\(c.b\left(a-c\right)+5a-5c=b\left(a-c\right)+5\left(a-c\right)=\left(a-c\right)\left(b+5\right)\)

\(d.a\left(m-n\right)+m-n=\left(m-n\right)\left(a+1\right)\)

\(e.mx+my+5x+5y=m\left(x+y\right)+5\left(x+y\right)=\left(x+y\right)\left(m+5\right)\)

\(f.ma+mb-a-b=m\left(a+b\right)-\left(a+b\right)=\left(a+b\right)\left(m-1\right)\)

\(g.4x+by+4y+bx=4x+bx+by+4y=x\left(b+4\right)+y\left(b+4\right)=\left(b+4\right)\left(x+y\right)\)

\(h.1-ax-x+a=\left(a+1\right)-x\left(a+1\right)=\left(a+1\right)\left(1-x\right)\)

\(k.x^{m+2}-x^m=x^m\left(x^2-1\right)=x^m\left(x-1\right)\left(x+1\right)\)

\(m.\left(a-b\right)^2-\left(b-a\right)\left(a+b\right)=\left(b-a\right)^2-\left(b-a\right)\left(a+b\right)=\left(b-a\right)\left(b-a-a-b\right)=-2a\left(b-a\right)\)

\(n.a\left(a-b\right)\left(a+b\right)-\left(a^2-2ab+b^2\right)=a\left(a-b\right)\left(a+b\right)-\left(a-b\right)^2=\left(a-b\right)\left(a^2+ab-a+b\right)\)