Question

若a²+ b²=6，则代数式(3a²-2ab-b²)-(a²-2ab-3b²)的值为____。

Answer 1

(3a²-2ab-b²)-(a²-2ab-3b²)
=3a²-2ab-b²-a²+2ab-+b²
=2a²+ 2b²
=2（a²+ b²）
把a²+ b²=6带入
2（a²+ b²）=2*6=12

Answer 2

原式=(a-b)(3a+b)-(a-3b)(a+b)=(a-b)(a+b+2a)-(a-b-2b)(a+b)
=(a²-b²)+2a(a-b)-(a²-b²)+2b(a+b)=2a(a-b)+2b(a+b)=2a²-2ab+2ab+2b²=2(a²+b²)=2×6=12