(-3a-2b)² 已知A=2x+y,B=2x-y,计算A²-B²

(-3a-2b)² 已知A=2x+y,B=2x-y,计算A²-B²

(-3a-2b)²=9a²+12ab+4b²
A²-B²=(A+B)(A-B)=(2x+y+2x-y)(2x+y-2x+y)=4x*2y=8xy

1.A=2x+y
2.B=2x-y
1与2联立
1式-2式：A-B=2y；
1式+2式：A+B=4x
则：A²-B²=（A-B)(A+B)=2y*4x=8xy

(-3a-2b)²=(3a+2b)²
=9a²+12ab+4b²
A²-B²=(2x+y)²-(2x-y)²
=(4x²+4xy+y²)-(4x²-4xy+y²)
=4x²+4xy+...

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(-3a-2b)²=(3a+2b)²
=9a²+12ab+4b²
A²-B²=(2x+y)²-(2x-y)²
=(4x²+4xy+y²)-(4x²-4xy+y²)
=4x²+4xy+y²-4x²+4xy-y²)
=8xy
另一法
A²-B²=(A+B)(A-B)
=(2x+y+2x-y)(2x+y-2x+y)
=4x*2y
=8xy

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