问题
计算题
计算:(a+b)2(c+d)2﹣2(a2﹣b2)(c2﹣d2)+(a﹣b)2(c﹣d)2
答案
解:原式=(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+ad+bc+bd﹣(ac﹣ad﹣bc+bd)]2
=(2ad+2bc)2
=4a2d2+8abcd+4b2c2
计算:(a+b)2(c+d)2﹣2(a2﹣b2)(c2﹣d2)+(a﹣b)2(c﹣d)2
解:原式=(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+ad+bc+bd﹣(ac﹣ad﹣bc+bd)]2
=(2ad+2bc)2
=4a2d2+8abcd+4b2c2