已知a+b=-2,a-b=2,把(a²+b²-1)²-4a²b²先分解因式,再求值
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![已知a+b=-2,a-b=2,把(a²+b²-1)²-4a²b²先分解因式,再求值](/uploads/image/z/14445217-1-7.jpg?t=%E5%B7%B2%E7%9F%A5a%2Bb%3D-2%2Ca-b%3D2%2C%E6%8A%8A%EF%BC%88a%26sup2%3B%2Bb%26sup2%3B-1%29%26sup2%3B-4a%26sup2%3Bb%26sup2%3B%E5%85%88%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F%2C%E5%86%8D%E6%B1%82%E5%80%BC)
已知a+b=-2,a-b=2,把(a²+b²-1)²-4a²b²先分解因式,再求值
已知a+b=-2,a-b=2,把(a²+b²-1)²-4a²b²先分解因式,再求值
已知a+b=-2,a-b=2,把(a²+b²-1)²-4a²b²先分解因式,再求值
(a²+b²-1)²-4a²b²
=(a²+b²-1)²-(2ab)²
=(a²+b²-1+2ab) *(a²+b²-1-2ab)
=[(a+b)^2-1] * [(a-b)^2-1]
=(4-1)*(4-1)
=9
=[(a2+b2)2-1]2-4a2b2
=a4+b4+2a2b2+1-2a2-2b2-4a2b2
=a4+b4-2a2b2+1-2a2-2b2
由已知得:a=0 b=-2代入上式
得:9