因式分解(ab+cd)(a^2-b^2+c^2-d^2)+(ac+bd)(a^2+b^2-……因式分解(ab+cd)(a^2-b^2+c^2-d^2)+(ac+bd)(a^2+b^2-c^2-d^2)过程清楚,不要跳步

Question

因式分解(ab+cd)(a^2-b^2+c^2-d^2)+(ac+bd)(a^2+b^2-……
因式分解(ab+cd)(a^2-b^2+c^2-d^2)+(ac+bd)(a^2+b^2-
c^2-d^2)
过程清楚,不要跳步

Answer 1

(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)