已知a²+2ab=－8,b²+2ab=14,则a²+4ab+b²=______ ;a²-b²=________.

已知a²+2ab=－8,b²+2ab=14,则a²+4ab+b²=______ ;a²-b²=________.
已知a²+2ab=－8,b²+2ab=14,则a²+4ab+b²=______ ;a²-b²=________.

已知a²+2ab=－8,b²+2ab=14,则a²+4ab+b²=______ ;a²-b²=________.
a²+4ab+b²
=a²+2ab+2ab+b²
=(a²+2ab)+(b²+2ab)
=-8+14
=6
a²-b²
=a²+2ab-2ab-b²
=(a²+2ab)-(b²+2ab)
=-8-14
=-22

a²+2ab=－8,……（1）
b²+2ab=14……（2）
（1)+(2)得：a²+4ab+b²=-8+14
a²+4ab+b²=6
(或：a²+4ab+b²
=a²+2ab+b²+2ab
=-8+14
=6)
2、a²-b²
=a²+2ab-b²-2ab
=a²+2ab-(b²+2ab)
=-8-14
=-22

a²+2ab=－8, ①
b²+2ab=14,②
∴①+②
a²+2ab+b²+2ab=-8+14
即：a²+4ab+b²=6
①-②
a²+2ab-b²-2ab=-8-14
a²-b²=-22