Factorise$$4(ab+cd)^2-\left(a^2+b^2-c^2-d^2\right)^2$$
I can't solve this math assignment from my text book. No one knows how to solve it, so I would be so thankful to you if you presented your step-by-step solution. Thank you very much and I know this is probably an easy question for you, but I don't know the answer to it.
$$4(ab+cd)^2-(a^2+b^2-c^2-d^2)^2=$$ $$(2(ab+cd)-a^2-b^2+c^2+d^2)(2(ab+cd)+a^2+b^2-c^2-d^2)=$$ $$=((c+d)^2-(a-b)^2)((a+b)^2-(c-d)^2)=$$ $$=(c+d-a+b)(c+d+a-b)(a+b-c+d)(a+b+c-d).$$