因式分解(ab+cd)(a^2-b^2+c^2-d^2)+(ac+bd)(a^2+b^2-……

(ab+cd)(a²-b²+c²-d²)+(ac+bd)(a²+b²-c²-d²)
=(ab+cd)(a²-d²)-(ab+cd)(b²-c²)+(ac+bd)(a²-d²)+(ac+bd)(b²-c²)
=(ab+cd+ac+bd)(a²-d²)+(ac+bd-ab-cd)(b²-c²)
=(a+d)(b+c)(a+d)(a-d)+(a-d)(c-b)(b+c)(b-c)
=(a-d)(b+c)[(a+d)²-(b+c)²]
=(a-d)(b+c)(a+d+b+c)(a+d-b-c)

=a^3b-ab^3+abc^2-abd^2+a^2cd-b^2cd+c^3d+cd^3+a^3c+ab^2c-ac^3-acd^2+a^2bd+b^3d-c^2bd-bd^3
=a^3(b+c)+b^3(d-a)+c^3(d-a)-d^3(b+c)+abc(b+c)-abd(d-a)-acd(d-a)-bcd(b+c)
=(b+c)(a^3-d^3+abc-bcd)+(d-a)(b^3+c^3-abd-acd)
=(b+c)(a-d)(a^2+d^2+ad+bc)+(d-a)(b+c)(b^2+c^2-bc-ad)
=(b+c)(a-d)(a^2+d^2+2ad+2bc-b^2-c^2)
=(b+c)(a-d)[(a+d)^2-(b-c)^2]
=(b+c)(a-d)(a+d+b-c)(a+d-b+c)