(a-b)(a+b)²-(a+b)(a-b)²+2b(a²+b²) 分解因式
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![(a-b)(a+b)²-(a+b)(a-b)²+2b(a²+b²) 分解因式](/uploads/image/z/2590750-46-0.jpg?t=%28a-b%29%28a%2Bb%29%26%23178%3B-%28a%2Bb%29%28a-b%29%26%23178%3B%2B2b%28a%26%23178%3B%2Bb%26%23178%3B%29+%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F)
(a-b)(a+b)²-(a+b)(a-b)²+2b(a²+b²) 分解因式
(a-b)(a+b)²-(a+b)(a-b)²+2b(a²+b²) 分解因式
(a-b)(a+b)²-(a+b)(a-b)²+2b(a²+b²) 分解因式
第一步,前两项提取(a-b)
=(a-b)[(a+b)2-(a+b)(a-b)]+2b(a2+b2)
=(a-b)[a2+2ab+b2-(a2-b2)]+2b(a2+b2)
=(a-b)(2ab+2b2)+2b(a2+b2)
=2b[(a-b)(a+b)] +2b(a2+b2)
=2b[(a2-b2)+(a2+b2)]
=2b*2a2
=4a2b