Question

已知a+b=-2,a-b=2把(a^2+b^2-1)^2-4a^2b^2 先分解因式，再求值。

Answer 1

(a^2+b^2-1)^2-4a^2b^2 =(a^2+b^2-1+2ab)(a^2+b^2-1-2ab)=[(a+b)^2-1][(a-b)^2-1]
将a+b=-2,a-b=2代入[(a+b)^2-1][(a-b)^2-1]得
[(a+b)^2-1][(a-b)^2-1]=[(-2)^2-1][2^2-1]=9
故所求值是9

Answer 2

(a²+b²-1)²-4a²b²
=(a²+b²-1+2ab)(a²+b²+1-2ab)
=[(a+b)²-1][(a-b)²-1]
=(4-1)(4-1)
=9