因式分解:(x+y)²+4(x-y)²-4(x²-y²)
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因式分解:(x+y)²+4(x-y)²-4(x²-y²)
![因式分解:(x+y)²+4(x-y)²-4(x²-y²)](/uploads/image/z/16086544-16-4.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%EF%BC%9A%28x%2By%29%26%23178%3B%2B4%28x-y%29%26%23178%3B-4%28x%26%23178%3B-y%26%23178%3B%29)
(x+y)²+4(x-y)²-4(x²-y²)
=(x+y)²-2×(x+y)(x-y)+[2(x-y)]²
=[(x+y)-2(x-y)]²
=(x+y-2x+2y)²
=(x-3y)²
=(x+y)²-2×(x+y)(x-y)+[2(x-y)]²
=[(x+y)-2(x-y)]²
=(x+y-2x+2y)²
=(x-3y)²