因式分解(a²+ab+b²)²-9a²b²,
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因式分解(a²+ab+b²)²-9a²b²,
![因式分解(a²+ab+b²)²-9a²b²,](/uploads/image/z/18233574-6-4.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%28a%26%23178%3B%2Bab%2Bb%26%23178%3B%29%26%23178%3B-9a%26%23178%3Bb%26%23178%3B%2C)
答:
先用平方差公式:
(a²+ab+b²)²-9a²b²
=(a²+ab+b²-3ab)(a²+ab+b²+3ab)
=(a²-2ab+b²)(a²+4ab+b²)
=(a-b)²(a²+4ab+b²)
先用平方差公式:
(a²+ab+b²)²-9a²b²
=(a²+ab+b²-3ab)(a²+ab+b²+3ab)
=(a²-2ab+b²)(a²+4ab+b²)
=(a-b)²(a²+4ab+b²)