·分式因解~Sos.1.4a^2b^2-(a^2+b^2-c^2)=?2.8+2(a^2+3a)-(a^2+3a)^2=?

Question

·分式因解~Sos.
1.4a^2b^2-(a^2+b^2-c^2)=?
2.8+2(a^2+3a)-(a^2+3a)^2=?

Answer 1

因为
a^2+b^2-4a^2b^2
=a^2+b^2-4a^2b^2+2ab-2ab
=(a+b)^2-4a^2b^2-2ab
=(a+b)^2-4a^2b^2-2ab+1/4-1/4
=(a+b)^2-(2ab+1/2)^2+1/4
=(a+b+2ab+1/2)(a+b-2ab-1/2)+1/4
所以
4a^2b^2-(a^2+b^2)
=-(a+b+2ab+1/2)(a+b-2ab-1/2)-1/4
提供一个思路把~后面的我也有点莫名...