a(a+1)-b(b-1)
=a^2+a-b^2+b
=(a+b)(a-b)+(a+b)
=(a+b)(a-b+1)
ax-ay+a^2+bx-by+ab
=(x-y)(a+b)+a(a+b)
=(a+b)(x-y+a)
ax-bx+cx-ay+by-cy
=x(a-b+c)-y(a-b+c)
=(x-y)(a-b+c)