因式分解:a^4-8a^2+16
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因式分解:a^4-8a^2+16
![因式分解:a^4-8a^2+16](/uploads/image/z/20207191-31-1.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%EF%BC%9Aa%5E4-8a%5E2%2B16)
a^4-8a^2+16
=(a²-4)²
=(a+2)²(a-2)²
再问: (a^2-ab)^2-(ab-b^2)^2
再答: (a^2-ab)^2-(ab-b^2)^2 =[(a²-ab)+(ab-b²)][(a²-ab)-(ab-b²)] =(a²-b²)(a²-2ab+b²) =(a-b)³(a+b)
=(a²-4)²
=(a+2)²(a-2)²
再问: (a^2-ab)^2-(ab-b^2)^2
再答: (a^2-ab)^2-(ab-b^2)^2 =[(a²-ab)+(ab-b²)][(a²-ab)-(ab-b²)] =(a²-b²)(a²-2ab+b²) =(a-b)³(a+b)