2(a方+b方)(a+b)方-(a方-b方)方

来源:百度知道 编辑:UC知道 时间:2024/06/04 10:17:00
2(a方+b方)(a+b)方-(a方-b方)方 怎么分解啊

2(a²+b²)(a+b)²-(a²-b²)²
=2(a²+b²)(a+b)²-[(a+b)(a-b)]²
=2(a²+b²)(a+b)²-(a+b)²(a-b)²
=(a+b)²[2(a²+b²)-(a-b)²]
=(a+b)²(2a²+2b²-a²+2ab-b²)
=(a+b)²(a²+b²+2ab)
=(a+b)²(a+b)²
=(a+b)⁴

用到的公式:
a²-b²=(a+b)(a-b)
a²+2ab+b²=(a+b)²

=2(A方+B方)(A+B)方-(A+B)方(A-B)方
=(A+B)方[2(A方+B方)-(A-B)方]
=(A+B)方(2A方+2B方-A方-B方+2AB)
=(A+B)方(A+B)方
=(A+B)四

2(a方+b方)(a+b)方-(a方-b方)方
=2(a方+b方)(a+b)方-(a+b)方(a-b)方
=(a+b)方【2(a方+b方)-(a-b)方】
=(a+b)方(2a方+2b方-a方+2ab-b方)
=(a+b)方(a+b)方
=(a+b)四次方

(a方-b方)=(a+b)(a-b),提取公因式(a+b)不就可以了?下面不写了,自己动脑筋吧

2(a方+b方)*(a方+B方+2AB)-(A+B)*(A-B)
=提取公因式(a+b)

好复杂呃 不过答案是(a+b)³