(a+b)(a2+ab+b2)+(a-b)(a2-ab+b2)怎么算?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 10:08:56
![(a+b)(a2+ab+b2)+(a-b)(a2-ab+b2)怎么算?](/uploads/image/z/6881916-12-6.jpg?t=%28a%2Bb%29%28a2%2Bab%2Bb2%29%2B%28a-b%29%28a2-ab%2Bb2%29%E6%80%8E%E4%B9%88%E7%AE%97%3F)
(a+b)(a2+ab+b2)+(a-b)(a2-ab+b2)怎么算?
(a+b)(a2+ab+b2)+(a-b)(a2-ab+b2)
怎么算?
(a+b)(a2+ab+b2)+(a-b)(a2-ab+b2)怎么算?
(a+b)(a^2+ab+b^2)+(a-b)(a^2-ab+b^2)
=a^3+a^2b+ab^2+a^2b+ab^2+b^3+a^3-a^2b+ab^2-a^2b+ab^2-b^3
=2a^3+4ab^2
(a+b)(a2+ab+b2)+(a-b)(a2-ab+b2)
=a^3+a^2b+ab^2+a^2b+ab^2+b^3+a^3-a^2b+ab^2-a^2b+ab^2-b^3
=2a^3+4ab^2
=2a(a^2+2b^2)
(a+b)(a^2+ab+b^2)+(a-b)(a^2-ab+b^2)
=(a+b)[(a^2+b^2)+ab]+(a-b)[(a^2+b^2)-ab]
=(a+b)(a^2+b^2)+ab(a+b)+(a-b)(a^2+b^2)-ab(a-b)
=(a^2+b^2)[(a+b)-(a-b)]+ab[(a+b)-(a-b)]
=2b(a^2+b^2+ab)
=2a^2b+2b^3+2ab^2
答案是:2a^3+4ab^2
过程可以稍微简化一点:
(a+b)(a^2+ab+b^2)+(a-b)(a^2-ab+b^2)
=(a+b)(a^2-ab+b^2+2ab)+(a-b)(a^2+ab+b^2-2ab)
=(a+b)(a^2-ab+b^2)+2ab(a+b)+(a-b)(a^2+ab+b^2)-2ab(a-b)
=a^3+b^3+2a^2b+2ab^2+a^3-b^3-2a^2b+2ab^2
=2a^3+4ab^2
你看有问题吗?