Question

(a+b)²（c+d)²-2(a²-b²)(c²-d²)+(a-b)²(c-d)²

简便算法

Answer 1

套完全平方公式，现在的两项分别是(a+b)(c+d)和(a-b)(c-d)
(a+b)²(c+d)²-2(a²-b²)(c²-d²)+(a-b)²(c-d)²
=(a+b)²(c+d)²-2(a+b)(a-b)(c+d)(c-d)+(a-b)²(c-d)²
=[(a+b)(c+d)-(a-b)(c-d)]²
=[(ac+bc+ad+bd)-(ac-bc-ad+bd)]²
=(2bc+2ad)²
=4(bc+ad)²

Answer 2

(a+b)²（c+d)²-2(a²-b²)(c²-d²)+(a-b)²(c-d)² =[(a+b)(c+d)]²-2(a+b)(c+d)(a-b)(c-d)+[(a-b)(c-d)]² =[(a+b)(c+d)-(a-b)(c-d)]² =[(ac+ad+bc+bd)-(ac-ad-bc+bd)]² =(2ad+2bc)² =4(ad+bc)²