已知x=a+b,y=a-b,求(x²+y²)²-(x²-y²)²的值

已知x=a+b,y=a-b,求(x²+y²)²-(x²-y²)²的值
已知x=a+b,y=a-b,求(x²+y²)²-(x²-y²)²的值

已知x=a+b,y=a-b,求(x²+y²)²-(x²-y²)²的值
原式=[(x²+y²)+(x²-y²)][(x²+y²)-(x²-y²)]
=)2x1N)(2y²)
=4(xy)²
=4[(a+b)(a-b)]²
=4(a²-b²)²
=4a^4-8a²b²+4b^4

∵x=a+b,y=a-b
∴xy=(a+b)(a-b)=a²-b²
∴(x²+y²)²-(x²-y²)²
=x⁴+2x²y²+y⁴-x⁴+2x²y²-y⁴
=4x²y²
=4(a²-b²)²
=4a⁴-8a²b²+4b⁴

﹙x²＋y²﹚²－﹙x²－y²﹚²
＝﹙x²＋y²＋x²－y²﹚﹙x²＋y²－x²＋y²﹚
＝4x²y²
＝4﹙a＋b﹚²﹙a－b﹚²
＝[2﹙a²－b²]²