Question

已知A+B=2,则（A²-B²）²-8（A²+B²）的值是

Answer 1

（A²-B²）²=[(a+b)(a-b)]²=4(a-b)²

A²+B²=[(a+b)²+(a-b)²]/2=2+(a-b)²/2

（A²-B²）²-8（A²+B²）=4(a-b)²-8[2+(a-b)²/2]=4(a-b)²-16-4(a-b)²=-16