((a+b)(a-b))^2=(a+b)^2*(a-b)^2
=(a^2+2ab+b^2)(a^2-2ab+b^2)
所以
[((a+b)(a-b))^2]/(a^2+2ab+b^2)+2ab
=(a^2-2ab+b^2)+2ab
=a^2+b^2.
((a+b)(a-b))^2=(a+b)^2*(a-b)^2
=(a^2+2ab+b^2)(a^2-2ab+b^2)
所以
[((a+b)(a-b))^2]/(a^2+2ab+b^2)+2ab
=(a^2-2ab+b^2)+2ab
=a^2+b^2.